Journal of Numerical Analysis and Approximation Theory
type: channel
description: Founded in 1972, Journal of Numerical Analysis and Approximation Theory is an open access, single-blind peer-reviewed journal which publishes original and survey papers in all areas of Numerical Analysis and Approximation Theory. The journal is edited by Tiberiu Popoviciu Institute of Numerical Analysis (Romanian Academy) and published by the Publishing House of the Romanian Academy (Editura Academiei Române). Its former name is Revue d'analyse numérique et de théorie de l'approximation (see the history section). ISSN 2457-6794, ISSN-E 2501-059X
publisher: Editura Academiei Române
language: en
publication name: Journal of Numerical Analysis and Approximation Theory
issn: 2457-6794
copyright: Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
items: Two step Steffensen-type methods with or without memory for nondifferentiable equations
items: Reconstruction inversion formulas for the Laguerre Gabor transform
items: Laurent operator-based representation of discrete solutions in the Newmark scheme with non-homogeneous terms
items: Modified adaptive quadrature by expansion for Laplace and Helmholtz layer potentials in 2D
items: On the coordinate system-dependence of the accuracy of symplectic numerical methods
items: Applications of the theory of generalized Fourier transforms to Tikhonov problems
items: Some simple full-range inverse-normal approximations
items: Best approximation of Hartley-Bessel multiplier operators on weighted Sobolev spaces
items: Stability of piecewise flat Ricci flow in three dimensions
items: Upper and lower solution method for control of second-order Kolmogorov type systems
items: Book reviews
items: A simplified homotopy perturbation method for solving nonlinear ill-posed operator equations in Hilbert spaces
items: Products of parametric extensions: refined estimates
items: A numerical approach for singularly perturbed parabolic reaction-diffusion problem on a modified graded mesh
items: A comparative study on balanced truncation and projection onto the dominant eigenspace of the Gramian using Laguerre functions
items: A stable finite difference scheme for fractional viscoelastic wave propagation in space-time domain
items: Extended convergence of two-step iterative methods for solving equations with applications
items: On generation and properties of triple sequence-induced frames in Hilbert spaces
items: A new preconditioned Richardson iterative method
items: Convergence of the θ-Euler-Maruyama method for a class of stochastic Volterra integro-diﬀerential equations
items: A numerical study of an infeasible interior-point algorithm for convex quadratic semi-definite optimization
items: Falkner hybrid block methods for second-order IVPs: A novel approach to enhancing accuracy and stability properties
items: Exponential B-spline collocation method for singularly perturbed time-fractional delay parabolic reaction-diffusion equations
items: Numerical analysis and stability of the Moore-Gibson-Thompson-Fourier model
items: Higher-order approximations for space-fractional diffusion equation
items: Chebfun approximation to structure of positive radial solutions for a class of supercritical semi-linear Dirichlet problems
items: Additive operator splitting scheme for a general mean curvature flow and application in edges enhancement
items: Lebesgue constants for Cantor sets. Numerical results
items: A comparative study of Filon-type rules for oscillatory integrals

Two step Steffensen-type methods with or without memory for nondifferentiable equations
type: item
description: A wide range of applications emerging from diverse disciplines are formulated as an equation or system of equations in abstract spaces such as Euclidean multidimensional, Hilbert or Banach to mention a few, a plethora of which are nondifferentiable. Different methodologies are developed worldwide to handle the solutions of such equations. Such methodologies can also be applied to solve the differentiable equations. In the current study, two step Steffensen-Type methods with and without memory free from derivatives are considered for the nondifferentiable equations and the local as well as semilocal convergence analysis is proved under more generalized conditions. Numerical applications are provided which demonstrate the theoretical results. Better results in terms of radii of convergence balls and number of iterations are obtained using the proposed approach as compared to the existing ones.
subject: Articles
  topic: section
subject: divided difference
  topic: keywords
subject: Banach space
  topic: keywords
subject: Convergence
  topic: keywords
subject: Steffensen-type method
  topic: keywords
creator: Ioannis K. Argyros
creator: Gagan Deep
rights: Copyright (c) 2025 Ioannis K. Argyros, Gagan Deep https://creativecommons.org/licenses/by/4.0
date: 2025-10-03
publication date: 2025-10-03
doi: 10.33993/jnaat542-1457

Reconstruction inversion formulas for the Laguerre Gabor transform
type: item
description: In this paper, we define and study the Gabor transform in the context of the Laguerre hypergroup. We prove some of its basic properties, such as Plancherel theorem, inversion formula and Calder´on’s reproducing inversion formula. Next, using the harmonic analysis related to Laguerre hypergroup, we examine spaces of Sobolev type for which we make explicit kernels reproducing. Exploiting the aforesaid theory, we introduce and study the extremal function associated with the Gabor transform. Finally, by utilizing the reproducing kernels we establish important estimates for this extremal function.
subject: Articles
  topic: section
subject: Laguerre hypergroup
  topic: keywords
subject: Laguerre-Gabor transform
  topic: keywords
subject: Hilbert space
  topic: keywords
subject: reproducing kernel
  topic: keywords
subject: extremal function
  topic: keywords
creator: Khaled Hleili
creator: Manel Hleili
rights: Copyright (c) 2025 Khaled Hleili, Manel Hleili https://creativecommons.org/licenses/by/4.0
date: 2025-09-20
publication date: 2025-09-20
doi: 10.33993/jnaat542-1558

Laurent operator-based representation of discrete solutions in the Newmark scheme with non-homogeneous terms
type: item
description: This paper investigates representation results for second-order evolution equations arising in structural dynamics, discretized using the Newmark time integration scheme. More precisely, the discrete solution is expressed in terms of bi-infinite Toeplitz or Laurent operators. A spectral analysis of the associated discrete operators is discussed, and a convergence analysis is performed under relaxed regularity assumptions on the source term. Furthermore, we examine the errors introduced by some truncation strategies, including one that is commonly used in engineering practice.
subject: Articles
  topic: section
subject: Newmark time scheme
  topic: keywords
subject: Laurent operator
  topic: keywords
subject: spectral analysis
  topic: keywords
subject: error estimate
  topic: keywords
subject: convergence analysis
  topic: keywords
subject: 65L06
  topic: subjects
subject: 47B35
  topic: subjects
creator: Eliass Zafati
rights: Copyright (c) 2025 Eliass Zafati https://creativecommons.org/licenses/by/4.0
date: 2025-09-19
publication date: 2025-09-19
doi: 10.33993/jnaat542-1569

Modified adaptive quadrature by expansion for Laplace and Helmholtz layer potentials in 2D
type: item
description: An adaptive algorithm based on quadrature by expansion (QBX) is proposed for computing layer potentials at target points near or on a smooth boundary in \(\mathbb{R}^2\). The algorithm can be viewed as major modifications to the two-phase algorithm AQBX, proposed recently by Klinteberg et al. [SIAM Journal on Scientific Computing, 40(3), 2018]. In the modified AQBX (MAQBX), we consider sharper bounds for the involved truncation error. As a result, the involved stopping criteria are met earlier, and the total computational cost is reduced. Moreover, MAQBX is a single-phase algorithm and its structure is far simpler than that of AQBX. It is recommended that QBX (or any version of it) should be applied on a small part of the boundary that is near the target point, and a classical quadrature is applied on the rest of the boundary (this is often referred to as local QBX). We partially show that for Laplace and Helmholtz potentials, parametric symmetricity of the target point with respect to the near part, can improve the convergence of QBX. Based on this observation, we suggest the local MAQBX that is very efficient in practice both for computing layer potentials and for solving boundary integral equations via the Nystr\"{o}m scheme.
subject: Articles
  topic: section
subject: quadrature by expansion
  topic: keywords
subject: layer potential
  topic: keywords
subject: Laplace problem
  topic: keywords
subject: Helmholtz problem
  topic: keywords
subject: adaptive quadrature
  topic: keywords
creator: Hassan Majidian
rights: Copyright (c) 2025 Hassan Majidian https://creativecommons.org/licenses/by/4.0
date: 2025-09-16
publication date: 2025-09-16
doi: 10.33993/jnaat542-1572

On the coordinate system-dependence of the accuracy of symplectic numerical methods
type: item
description: Symplectic numerical methods have become a widely-used choice for the accurate simulation of Hamiltonian systems in various fields, including celestial mechanics, molecular dynamics and robotics. Even though their characteristics are well-understood mathematically, relatively little attention has been paid in general to the practical aspect of how the choice of coordinates affects the accuracy of the numerical results, even though the consequences can be computationally significant. The present article aims to fill this gap by giving a systematic overview of how coordinate transformations can influence the results of simulations performed using symplectic methods. We give a derivation for the non-invariance of the modified Hamiltonian of symplectic methods under coordinate transformations, as well as a sufficient condition for the non-preservation of a first integral corresponding to a cyclic coordinate for the symplectic Euler method. We also consider the possibility of finding order-compensating coordinate transformations that improve the order of accuracy of a numerical method. Various numerical examples are presented throughout.
subject: Articles
  topic: section
subject: Symplectic numerical method
  topic: keywords
subject: processing
  topic: keywords
subject: Hamiltonian system
  topic: keywords
subject: coordinate transformation
  topic: keywords
subject: canonical transformation
  topic: keywords
subject: symplectic numerical method
  topic: subjects
subject: processing
  topic: subjects
subject: Hamiltonian system
  topic: subjects
subject: coordinate transformation
  topic: subjects
subject: canonical transformation
  topic: subjects
subject: 65P10
  topic: subjects
subject: 70H15
  topic: subjects
subject: 34A05
  topic: subjects
creator: Donát M. Takács
creator: Tamás Fülöp
rights: Copyright (c) 2025 Donát M. Takács, Tamás Fülöp https://creativecommons.org/licenses/by/4.0
date: 2025-09-11
publication date: 2025-09-11
doi: 10.33993/jnaat542-1577

Applications of the theory of generalized Fourier transforms to Tikhonov problems
type: item
description: We define and study multiplier operators associated with the Sturm-Liouville operator involving a nonnegative function satisfying certain conditions. We introduce and study the extremal function, and we deduce approximate inversion formulas for the multipliers operators in a Paley-Wiener type space.
subject: Articles
  topic: section
subject: SL-multiplier operators
  topic: keywords
subject: Paley-Wiener type space
  topic: keywords
subject: approximate inversion formulas
  topic: keywords
subject: SL-multiplier operators; Paley-Wiener type space; approximate inversion formulas
  topic: subjects
creator: Fethi Soltani
creator: Akram Nemri
rights: Copyright (c) 2025 Fethi Soltani, Akram Nemri https://creativecommons.org/licenses/by/4.0
date: 2025-06-30
publication date: 2025-06-30
starting page: 170
ending page: 190
doi: 10.33993/jnaat541-1539

Some simple full-range inverse-normal approximations
type: item
description: Two approximations are given for numerically inverting the full range of the standard normal cumulative distribution function. The first approximation has two fitted constants and only modest accuracy but is very simple and well suited for hand calculators. The second approximation has four fitted constants and is more accurate. Alternate versions of the approximations are also given, with the constants chosen to minimize the maximum relative error in the implied approximate q rather than the maximum absolute error in the approximate z.
subject: Articles
  topic: section
subject: numerical approximation
  topic: keywords
subject: inverse normal distribution function
  topic: keywords
subject: inverse error function
  topic: keywords
creator: Raymond Koopman
rights: Copyright (c) 2025 Raymond Koopman https://creativecommons.org/licenses/by/4.0
date: 2025-06-30
publication date: 2025-06-30
starting page: 111
ending page: 116
doi: 10.33993/jnaat541-1434

Best approximation of Hartley-Bessel multiplier operators on weighted Sobolev spaces
type: item
description: The main goal of this paper is to introduce the Hartley-Bessel \(L^2_\alpha\)-multiplier operators and to give for them some new results as Plancherel’s, Calderon’s reproducing formulas and Heisenberg’s, Donoho-Stark’s uncertainty principles. Next, using the theory of reproducing kernels we give best approximation and an integral representation of the extremal functions related to these operators on weighted Sobolev spaces.
subject: Articles
  topic: section
subject: Hartley transform
  topic: keywords
subject: Bessel functions
  topic: keywords
subject: Calder´on’s reproducing formulas
  topic: keywords
subject: Approximation theory
  topic: keywords
creator: Ahmed Chana
creator: Abdellatif Akhlidj
rights: Copyright (c) 2025 Ahmed Chana, Abdellatif Akhlidj https://creativecommons.org/licenses/by/4.0
date: 2025-06-30
publication date: 2025-06-30
starting page: 26
ending page: 41
doi: 10.33993/jnaat541-1512

Stability of piecewise flat Ricci flow in three dimensions
type: item
description: For a recently developed piecewise flat approximation of the Ricci flow, numerical instabilities are seen to arise for a particularly useful class of mesh-types. Here, a geometrically motivated adaptation to these meshes is introduced, and a linear stability analysis and numerical simulations used to show that the instability is then suppressed. These adapted meshes have also been successfully used in a recently published paper to show the convergence of the piecewise flat Ricci flow to known smooth Ricci flow solutions for a variety of manifolds.
subject: Articles
  topic: section
subject: Numerical Ricci flow, piecewise flat, linear stability
  topic: keywords
subject: Numerical Ricci flow, piecewise flat, linear stability
  topic: subjects
creator: Rory Conboye
rights: Copyright (c) 2025 Rory Conboye https://creativecommons.org/licenses/by/4.0
date: 2025-06-30
publication date: 2025-06-30
starting page: 42
ending page: 61
doi: 10.33993/jnaat541-1549

Upper and lower solution method for control of second-order Kolmogorov type systems
type: item
description: In this paper, an upper and lower solution method for the control of second-order Kolmogorov systems is introduced. Two iterative algorithms, one exact and one approximate, are proposed and their convergence is studied. The technique is based on Perov's fixed point theorem, matrices convergent to zero, and the use of Bielecki's norm.
subject: Articles
  topic: section
subject: Kolmogorov system
  topic: keywords
subject: control problem
  topic: keywords
subject: approximation algorithm
  topic: keywords
subject: 34H05
  topic: subjects
subject: 37N25
  topic: subjects
subject: 34A12
  topic: subjects
subject: 34K35
  topic: subjects
creator: Alexandru Hofman
rights: Copyright (c) 2025 Alexandru Hofman https://creativecommons.org/licenses/by/4.0
date: 2025-06-30
publication date: 2025-06-30
starting page: 100
ending page: 110
doi: 10.33993/jnaat541-1515

Book reviews
type: item
description: Andrei Stan: David L. Chopp, Introduction to High Performance Scientific Computing, SIAM, Philadelphia, 2019, ISSN: 9781611975642, ISSN (print): 9781611975635. Eduard Stefan Grigoriciuc: Samuel D. Conte, Carl De Boor, Elementary numerical analysis: an algorithmic approach, SIAM, Philadelphia, 2018, XXIV + 454 pp., ISBN 978-1-61197-519-2 (paperback), eISBN 978-1-61197-520-8 (ebook). Part of the Classics in Applied Mathematics series.
subject: Book Reviews
  topic: section
creator: JNAAT
rights: Copyright (c) 2025 JNAAT https://creativecommons.org/licenses/by/4.0
date: 2025-06-30
publication date: 2025-06-30
starting page: 191
ending page: 193
doi: 10.33993/jnaat541-1586

A simplified homotopy perturbation method for solving nonlinear ill-posed operator equations in Hilbert spaces
type: item
description: One popular regularization technique for handling both linear and nonlinear ill-posed problems is homotopy perturbation. In order to solve nonlinear ill-posed problems, we investigate an iteratively-regularized simplified version of the Homotopy perturbation approach in this study. We examine the method's thorough convergence analysis under typical circumstances, focusing on the nonlinearity and the convergence rate under a H\"{o}lder-type source condition. Lastly, numerical simulations are run to confirm the method's effectiveness.
subject: Articles
  topic: section
subject: Nonlinear ill-posed operator equations
  topic: keywords
subject: Iterative regularization methods
  topic: keywords
subject: Nonlinear operators on Hilbert spaces
  topic: keywords
subject: Convergence analysis
  topic: keywords
subject: Homotopy perturbation method
  topic: keywords
subject: 47A52
  topic: subjects
subject: 65J15
  topic: subjects
subject: 65J22
  topic: subjects
subject: 65F22
  topic: subjects
subject: 47J06
  topic: subjects
creator: Sharad Kumar Dixit
rights: Copyright (c) 2025 Sharad Kumar Dixit https://creativecommons.org/licenses/by/4.0
date: 2025-06-30
publication date: 2025-06-30
doi: 10.33993/jnaat541-1544

Products of parametric extensions: refined estimates
type: item
description: We present point wise estimates on approximation by bounded linear operators of real-valued continuous functions defined on the cartesian product of d compact intervals. The main purpose is to provide a unified theory to deal with pointwise estimates on approximation processes of the above type which are generated by the tensor product method. This will constitute an extension and a refinement of earlier work of Haussmann and Pottinger. As an example a new estimate for approximation by multivariate positive linear operators is given.
subject: Articles
  topic: section
subject: approximation theory
  topic: keywords
subject: tensor products
  topic: keywords
subject: linear positive operators
  topic: keywords
creator: Heiner Gonska
rights: Copyright (c) 2025 Heiner Gonska https://creativecommons.org/licenses/by/4.0
date: 2025-06-30
publication date: 2025-06-30
starting page: 74
ending page: 88
doi: 10.33993/jnaat541-1542

A numerical approach for singularly perturbed parabolic reaction-diffusion problem on a modified graded mesh
type: item
description: This paper addresses the numerical approximations of solutions for one dimensional parabolic singularly perturbed problems of reaction-diffusion type. The solution of this class of problems exhibit boundary layers on both sides of the domain. The proposed numerical method involves combining the backward Euler method on a uniform mesh for temporal discretization and an upwind finite difference scheme for spatial discretization on a modified graded mesh. The numerical solutions presented here are calculated using a modified graded mesh and the error bounds are rigorously assessed within the discrete maximum norm. The primary focus of this study is to underscore the crucial importance of utilizing a modified graded mesh to enhance the order of convergence in numerical solutions. The method demonstrates uniform convergence, with first-order accuracy in time and nearly second-order accuracy in space concerning the perturbation parameter. Theoretical findings are supported by numerical results presented in the paper.
subject: Articles
  topic: section
subject: Singular perturbation problem,
  topic: keywords
subject: Parabolic reaction-diffusion problems,
  topic: keywords
subject: Finite difference methods,
  topic: keywords
subject: Modified graded mesh,
  topic: keywords
subject: Boundary layers,
  topic: keywords
subject: Uniform convergence
  topic: keywords
creator: Kishun Kumar Sah
creator: Subramaniam Gowrisankar
rights: Copyright (c) 2025 Kishun Kumar Sah, Subramaniam Gowrisankar https://creativecommons.org/licenses/by/4.0
date: 2025-06-30
publication date: 2025-06-30
starting page: 117
ending page: 139
doi: 10.33993/jnaat541-1513

A comparative study on balanced truncation and projection onto the dominant eigenspace of the Gramian using Laguerre functions
type: item
description: This paper presents a comparative analysis of two model reduction techniques: balanced truncation and projection onto the dominant eigenspace of the Gramian. Both methods are evaluated through the lens of Laguerre functions which is a reduction technique based on Laguerre function expansion, that approximates the low-rank factors of the Controllability and Observability Gramians to produce approximately balanced systems without solving Lyapunov equations. We demonstrate the effectiveness of each approach in reducing the complexity of linear time-invariant (LTI) systems while preserving system dynamics. Numerical experiments highlight the strengths and weaknesses of both methods, showcasing their applicability to large-scale systems. By thoroughly analyzing both methods in conjunction with Laguerre functions, we contribute to the ongoing discourse in the field and lay the groundwork for future advancements in model reduction techniques.
subject: Articles
  topic: section
creator: Shafiqul Islam
creator: Saiduzzaman Sayed
creator: Monir Uddin
creator: Osman Gani
rights: Copyright (c) 2025 Shafiqul Islam , Saiduzzaman Sayed, Monir Uddin, Osman Gani https://creativecommons.org/licenses/by/4.0
date: 2025-06-30
publication date: 2025-06-30
starting page: 157
ending page: 169
doi: 10.33993/jnaat541-1525

A stable finite difference scheme for fractional viscoelastic wave propagation in space-time domain
type: item
description: This work focuses on the numerical approximation of the one dimensional wave propagation equation in a viscoelastic medium modelled by the fractional Zener model. First, we propose an explicit centred finite difference scheme. Then, we prove a sufficient stability condition for this scheme using an energy technique. Furthermore, we demonstrate that this condition is numerically necessary. Finally, we present various numerical simulations to validate the proposed scheme.
subject: Articles
  topic: section
subject: Caputo fractional derivative
  topic: keywords
subject: wave simulations
  topic: keywords
subject: Viscoelastic
  topic: keywords
subject: Finite-difference method
  topic: keywords
creator: Mohamed Ait ichou
creator: Abdelaaziz Ezziani
rights: Copyright (c) 2025 Mohamed Ait ichou, Abdelaaziz Ezziani https://creativecommons.org/licenses/by/4.0
date: 2025-06-30
publication date: 2025-06-30
starting page: 3
ending page: 25
doi: 10.33993/jnaat541-1530

Extended convergence of two-step iterative methods for solving equations with applications
type: item
description: The convergence of two-step iterative methods of third and fourth order of convergence are studied under weaker hypotheses than in earlier works using our new idea of the restricted convergence region. This way, we obtain a finer semilocal and local convergence analysis, and under the same or weaker hypotheses. Hence, we extend the applicability of these methods in cases not covered before. Numerical examples are used to compare our results favorably to earlier ones.
subject: Articles
  topic: section
subject: Banach space, restricted convergence region, convergence of iterative method.
  topic: keywords
subject: Mathematics
  topic: subjects
creator: Ioannis K. Argyros
creator: Santhosh George
rights: Copyright (c) 2024 Santhosh George, Ioannis K Argyros https://creativecommons.org/licenses/by/4.0
date: 2024-12-18
publication date: 2024-12-18
starting page: 187
ending page: 198
doi: 10.33993/jnaat532-1178

On generation and properties of triple sequence-induced frames in Hilbert spaces
type: item
description: In this paper, we present the innovative idea of ”t-frames,” frames produced by triple sequences within Hilbert spaces. The paper explores various properties of these t-frames, delving into topics like frame operators, alternative dual frames, and the stability inherent in t-frames.
subject: Articles
  topic: section
creator: Asif H. Jan
creator: Younis A. Bhat
creator: Tanweer Jalal
creator: Neyaz Sheikhh
rights: Copyright (c) 2024 Asif Hussain Jan, Tanweer Jalal, Younis Ahmad Bhat https://creativecommons.org/licenses/by/4.0
date: 2024-12-18
publication date: 2024-12-18
starting page: 259
ending page: 278
doi: 10.33993/jnaat532-1423

A new preconditioned Richardson iterative method
type: item
description: In this paper, we propose a new iterative technique for solving an operator equation \(Ax=y\) based on the Richardson iterative method. Then, by using the Chebyshev polynomials, we modify the proposed method to accelerate the convergence rate. Also, we present the results of some numerical experiments that demonstrate the efficiency and effectiveness of the proposed methods compared to the existing, state-of-the-art methods.
subject: Articles
  topic: section
subject: iterative method
  topic: keywords
subject: Richardson iteration
  topic: keywords
subject: convergence rate
  topic: keywords
subject: Chebyshev polynomials
  topic: keywords
creator: Hassan Jamali
creator: Reza Pourkani
rights: Copyright (c) 2024 Hassan Jamali, Reza Pourkani, Mohammad Abdi Arablou https://creativecommons.org/licenses/by/4.0
date: 2024-12-18
publication date: 2024-12-18
starting page: 242
ending page: 258
doi: 10.33993/jnaat532-1430

Convergence of the θ-Euler-Maruyama method for a class of stochastic Volterra integro-diﬀerential equations
type: item
description: This paper addresses the convergence analysis of the θ-Euler-Maruyama method for a class of stochastic Volterra integro-diﬀerential equations (SVIDEs). At ﬁrst, we discuss the existence, uniqueness, boundedness and H¨older continuity of the theoretical solution. Subsequently, the strong convergence order of the θ-Euler-Maruyama approach for SVIDEs is shown. Finally, we provided numerical examples to illustrate the theoretical results.
subject: Articles
  topic: section
subject: Stochastic Volterra integro-diﬀerential equations, Θ-Euler-Maruyama method, strong convergence, H¨older continuity.
  topic: keywords
subject: Numerical methods for solving stochastic differential equations and their application
  topic: subjects
creator: Samiha Mouchir
creator: Abdeldjalil Slama
rights: Copyright (c) 2024 Samiha Mouchir https://creativecommons.org/licenses/by/4.0
date: 2024-12-18
publication date: 2024-12-18
starting page: 298
ending page: 323
doi: 10.33993/jnaat532-1433

A numerical study of an infeasible interior-point algorithm for convex quadratic semi-definite optimization
type: item
description: The focus of this research is to apply primal-dual interior-point pathfollowing methods, specifically those derived from Newton’s method for solving convex quadratic semidefinite optimization (CQSDO) problems. In this paper, we present a numerical study of an infeasible primal-dual interior-point method for tackling this class of optimization problems. Unlike the feasible interior-point algorithms, the proposed algorithm can be start with any initial positive definite matrix and does not require the strictly feasible initial points. Under certain conditions, the Newton system is well defined and its Jacobian is nonsingular at the solution. For computing an iteration throughout the algorithm, a Newton direction and a step-size are determined. Here, our search direction is based on Alizadeh-Haeberly-Overton (AHO) symmetrization. However, for the step size along this direction an efficient procedure is suggested. Preliminary numerical results demonstrate the efficiency of our algorithm.
subject: Articles
  topic: section
subject: Convex quadratic semidefinite optimization, Interior-point methods, Primal-dual algorithm, Newton method.
  topic: keywords
creator: Yasmina Bendaas
creator: Mohamed Achache
rights: Copyright (c) 2024 Yasmina Bendaas, Mohamed Achache https://creativecommons.org/licenses/by/4.0
date: 2024-12-18
publication date: 2024-12-18
starting page: 199
ending page: 217
doi: 10.33993/jnaat532-1442

Falkner hybrid block methods for second-order IVPs: A novel approach to enhancing accuracy and stability properties
type: item
description: Second-order initial value problems (IVPs) in ordinary differential equations (ODEs) are ubiquitous in various fields, including physics, engineering, and economics. However, their numerical integration poses significant challenges, particularly when dealing with oscillatory or stiff problems. This article introduces a novel Falkner hybrid block method for the numerical integration of second-order IVPs in ODEs. The newly developed method is of order six with a large interval of absolute stability and is implemented using a fixed step size technique. The numerical experiments show the accuracy of our methods when compared with Falkner linear multistep methods, block methods, and other hybrid codes proposed in the scientific literature. This innovative approach demonstrates improved accuracy and stability in solving second-order IVPs, making it a valuable tool for researchers and practitioners.
subject: Articles
  topic: section
subject: Numerical analysis
  topic: subjects
creator: Robert I. Okuonghae
creator: Joshua K. Ozobokeme
rights: Copyright (c) 2024 Robert Okuonghae, Kaidi https://creativecommons.org/licenses/by/4.0
date: 2024-12-18
publication date: 2024-12-18
starting page: 324
ending page: 342
doi: 10.33993/jnaat532-1450

Exponential B-spline collocation method for singularly perturbed time-fractional delay parabolic reaction-diffusion equations
type: item
description: The singularly perturbed time-fractional delay parabolic reaction-diffusion of initial boundary value problem is provided by the present study. Employing implicit Euler's method along with the Caputo fractional derivative, the time-fractional is discretized. Spatial domain is handled by implementing the exponential B-spline collocation technique. The converge of the method is varified and has an accuracy of \(O(N^{-2}(lnN)^{2})\). Two model examples are examined in order to examine the extent to which the scheme is effective. The findings generated by tables and figures indicate the scheme has dual layers at the end spatial domain and is uniformly convergent.
subject: Articles
  topic: section
subject: Delay Parabolic reaction-diffusion, Time-fractional, Exponential B-spline Collocation Method
  topic: keywords
subject: Numerical analysis
  topic: subjects
creator: Feyisa E. Merga
creator: Gemechis F. Duressa
rights: Copyright (c) 2024 Feyisa Edosa Merga, G.F. Duressa https://creativecommons.org/licenses/by/4.0
date: 2024-12-18
publication date: 2024-12-18
starting page: 279
ending page: 297
doi: 10.33993/jnaat533-1454

Numerical analysis and stability of the Moore-Gibson-Thompson-Fourier model
type: item
description: This work is concerned the Moore-Gibson-Thompson-Fourier Model. Our contribution will consist in studying the numerical stability of the Moore-Gibson-Thompson-Fourier system. First we introduce a finite element approximation after the discretization, then we prove that the associated discrete energy decreases and later we establish a priori error estimates. Finally, we obtain some numerical simulations.
subject: Articles
  topic: section
creator: Ali Smouk
creator: Atika Radid
rights: Copyright (c) 2024 ALI SMOUK https://creativecommons.org/licenses/by/4.0
date: 2024-12-18
publication date: 2024-12-18
starting page: 343
ending page: 356
doi: 10.33993/jnaat532-1486

Higher-order approximations for space-fractional diffusion equation
type: item
description: Second-order and third-order finite difference approximations for fractional derivatives are derived from a recently proposed unified explicit form. The Crank-Nicholson schemes based on these approximations are applied to discretize the space-fractional diffusion equation. We theoretically analyse the convergence and stability of the Crank-Nicholson schemes, proving that they are unconditionally stable. These schemes exhibit unconditional stability and convergence for fractional derivatives of order in the range . Numerical examples further confirm the convergence order and unconditional stability of the approximations, demonstrating their effectiveness in practice.
subject: Articles
  topic: section
subject: Fractional derivatives, Grünwald approximation, Unified explicit form, Space Fractional diffusion equation
  topic: keywords
creator: Anura Gunarathna Wickramarachchi
creator: Haniffa Mohamed Nasir
rights: Copyright (c) 2024 W Anura Gunarathna, Haniffa Mohamed Nasir https://creativecommons.org/licenses/by/4.0
date: 2024-12-18
publication date: 2024-12-18
starting page: 357
ending page: 375
doi: 10.33993/jnaat532-1501

Chebfun approximation to structure of positive radial solutions for a class of supercritical semi-linear Dirichlet problems
type: item
description: We use the Chebfun programming package to approximate numerically the structure of the set of positive radial solutions for a class of supercritical semilinear elliptic Dirichlet boundary value problems. This structure (bifurcation diagram) is provided only at the heuristic level in many important works. In this paper, we investigate this structure, as accurately as possible, for the class of problems mentioned above taking into account the dimension of Euclidean space as well as the physical parameter involved.
subject: Articles
  topic: section
creator: Călin I. Gheorghiu
rights: Copyright (c) 2024 Calin-Ioan Gheorghiu https://creativecommons.org/licenses/by/4.0
date: 2024-12-18
publication date: 2024-12-18
starting page: 233
ending page: 241
doi: 10.33993/jnaat532-1503

Additive operator splitting scheme for a general mean curvature flow and application in edges enhancement
type: item
description: Many models that use non-linear partial differential equations (PDEs) have been extensively applied for different tasks in image processing. Among these PDE-based approaches, the mean curvature flow filtering has impressive results, for which feature directions in the image are important. In this paper, we explore a general model of mean curvature flow, as proposed in [4, 5]. The model can be re-arranged to a reaction-diffusion form, facilitating the creation of an unconditionally stable semi-implicit scheme for image filtering. The method employs the Additive Operator Split (AOS) technique. Experiments demonstrated that the modified general model of mean curvature flow is highly effective for reducing noise and has a superior job of preserving edges.
subject: Articles
  topic: section
subject: Nonlinear diffusion equations - Mean curvature flow - Additive operator splitting - Unconditionally stable schemes - Edge enhancement.
  topic: keywords
creator: Rafaa Chouder
creator: Noureddine Benhamidouche
rights: Copyright (c) 2024 benhamidouche noureddine, Chouder Rafaa https://creativecommons.org/licenses/by/4.0
date: 2024-12-18
publication date: 2024-12-18
starting page: 218
ending page: 232
doi: 10.33993/jnaat532-1504

Book reviews
type: item
description: Book reviews for: Brad G. Osgood, Lectures on the Fourier Transform and Its Applications, AMS, 2019, 693 pp., ISBN 978-1-4704-4191-3 (paperback), ISBN 978-1-4704-4976-6 (ebook). Reviewed by Călin Gheorghiu. Jeffrey Humpherys, Tyler J. Jarvis, Emily J. Evans, Foundations of Applied Mathematics. Volume 1: Mathematical Analysis, SIAM, Philadelphia, 2017, XX + 689 pp., ISBN 978-1-61197-489-8 (paperback), ISBN 978-1-61197-490-4 (ebook). Part of the Other Titles in Applied Mathematics series. Reviewed by Eduard Grigoriciuc. Jeffrey Humpherys, Tyler J. Jarvis, Foundations of Applied Mathematics. Volume 2: Algorithms, Approximation, Optimization, SIAM, Philadelphia, 2020, XVIII + 788 pp., ISBN 978-1-61197-605-2 (paperback), ISBN 978-1-61197-606-9 (ebook). Reviewed by Andra Malina. Ed Bueler, PETSc for Partial Differential Equations: Numerical Solutions in C and Python, SIAM, Philadelphia, 2020, XVI + 391 pp., ISBN 978-1-61197-630-4 (paperback), ISBN 978-1-61197-631-1 (ebook). Review by Mihai Nechita.
subject: Book Reviews
  topic: section
creator: jnaat
rights: Copyright (c) 2024 jnaat https://creativecommons.org/licenses/by/4.0
date: 2024-12-18
publication date: 2024-12-18
starting page: 376
ending page: 379
doi: 10.33993/jnaat532-1523

Lebesgue constants for Cantor sets. Numerical results
type: item
description: We analyze numerically the form of Lebesgue functions and the values of Lebesgue constants in polynomial interpolation for three types of Cantor sets.
subject: Articles
  topic: section
creator: Alexander Goncharov
creator: Yiğit Görgülü
creator: Yaman Paksoy
rights: Copyright (c) 2025 Alexander Goncharov, Yiğit Görgülü, Yaman Paksoy https://creativecommons.org/licenses/by/4.0
date: 2025-06-30
publication date: 2025-06-30
starting page: 62
ending page: 73
doi: 10.33993/jnaat541-1511

A comparative study of Filon-type rules for oscillatory integrals
type: item
description: Our aim is to answer the following question: "Among the Filon-type methods for computing oscillatory integrals, which one is the most efficient in practice?". We first discuss why we should seek the answer among the family of Filon-Clenshaw-Curtis rules. A theoretical analysis accompanied by a set of numerical experiments reveals that the plain Filon-Clenshaw-Curtis rules reach a given accuracy faster than the (adaptive) extended Filon-Clenshaw-Curtis rules. The comparison is based on the CPU run-time for certain wave numbers (medium and large).
subject: Articles
  topic: section
subject: oscillatory integral
  topic: keywords
subject: Filon-Clenshaw-Curtis rule
  topic: keywords
subject: extended FCC rule
  topic: keywords
subject: adaptive FCC rule
  topic: keywords
creator: Hassan Majidian
rights: Copyright (c) 2023 Hassan Majidian https://creativecommons.org/licenses/by/4.0
date: 2024-03-06
publication date: 2024-03-06
starting page: 130
ending page: 143
doi: 10.33993/jnaat531-1380