Browsing by Author "Gunes, B."

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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 Second-Order Difference Scheme for the Singularly Perturbed Sobolev Problems With Third Type Boundary Conditions on Bakhvalov Mesh
(Taylor & Francis Ltd, 2022) Gunes, B.; Duru, Hakki
We consider a singularly perturbed initial-third boundary value Sobolev problems. Firstly, the asymptotic behaviour of the exact solution is analysed. Then, a second-order finite difference scheme is constructed on the special non-uniform mesh. By using energy estimate, the stability and convergence of the proposed scheme are investigated in the discrete maximum norm. Finally, three numerical examples are solved to validate the theory.