Browsing by Author "Duru, H."

Now showing 1 - 4 of 4

A Computational Method for the Singularly Perturbed Delay Pseudo-Parabolic Differential Equations on Adaptive Mesh
(Taylor & Francis Ltd, 2023) Gunes, B.; Duru, H.
This paper aims to establish the finite difference scheme on Bakhvalov-type mesh for the singularly perturbed pseudo-parabolic problems with time-delay. Using the energy estimates, the bounds of the solution are investigated. An error analysis is derived in the discrete energy norm and the almost second order convergence is obtained. The reliability of the suggested method is displayed by means of a numerical example.
A Numerical Method for Solving Singularly Perturbed Quasilinear Boundary Value Problems on Shishkin Mesh
(Association of Mathematicians (MATDER), 2022) Duru, H.; Demirbas, M.
In this paper, singularly perturbed quasilinear boundary value problems are taken into account. With this purpose, a finite difference scheme is proposed on Shishkin-type mesh (S-mesh). Quasilinearization technique and interpolating quadrature rules are used to establish the numerical scheme. Then, an error estimate is derived. A numerical experiment is demonstrated to verify the theory. © MatDer.
A Numerical Scheme on S-Mesh for the Singularly Perturbed Initial Boundary Value Sobolev Problems With Large Time Delay
(Al-farabi Kazakh Natl Univ, 2023) Chiyaneh, A. B.; Duru, H.
The purpose of this article is to provide a numerical method for time delay singularly perturbed Sobolev type equations. First, asymptotic estimates for the Sobolev problem solution with singular perturbation and delay parameters were obtained. This estimate showed that the solution depends on the initial data. It is constructed and examined to solve this problem using a finite difference technique on a specific piecewise uniform mesh (Shishkin mesh)whose solution converges pointwise independent of the singular perturbation parameter. A discrete norm was used to investigate the stability of difference schemes. It is showed that the completely discrete scheme converges with order O (tau 2 + N-2 l l112 Nl) in both space and time, independent of the perturbation parameter. Finally, with a test problem and numerical experiments, the theoretical accuracy and computational effectiveness of the proposed methods are further testified.
A Robust Numerical Method for Singularly Perturbed Sobolev Periodic Problems on B-Mesh
(Al-farabi Kazakh Natl Univ, 2024) Duru, H.; Shazhdekeyeva, N.; Adiyeva, A.
This article examines periodic Sobolev reports with a singular deviation, which causes significant difficulties in numerical approximation due to the presence of sharp or boundary layers. A stable quantitative method for the effective solution of such problems in the Bakhvalov lattice, a special grid for the deviant action of the solution, is proposed. Singularly perturbed periodic Sobolev problems create significant difficulties in numerical approximation due to the presence of sharp layers or boundary layers. Our proposed reliable numerical method for efficiently solving such problems on the Bakhvalov grid, a specialized grid, is designed to account for the singular behavior of the solution. First, an asymptotic analysis of the exact solution is performed. Then a finite difference scheme is created by applying quadrature interpolation rules to an adaptive network. The stability and convergence of the presented algorithm in a discrete maximum norm is analyzed. The results show that the proposed approach provides an accurate approximation of the solution for singular problems while maintaining computational efficiency.