Browsing by Author "Amirali, Ilhame"

Now showing 1 - 4 of 4

Convergence Analysis of the Numerical Method for a Singularly Perturbed Periodical Boundary Value Problem
(int Scientific Research Publications, 2016) Cakir, Musa; Amirali, Ilhame; Kudu, Mustafa; Amiraliyev, Gabli M.
This work deals with the singularly perturbed periodical boundary value problem for a quasilinear second-order differential equation. The numerical method is constructed on piecewise uniform Shishkin type mesh, which gives first-order uniform convergence in the discrete maximum norm. Numerical results supporting the theory are presented. (C) 2016 All rights reserved.
High-Order Finite Difference Technique for Delay Pseudo-Parabolic Equations
(Elsevier Science Bv, 2017) Amiraliyev, Gabil M.; Cimen, Erkan; Amirali, Ilhame; Cakir, Musa
One dimensional initial boundary delay pseudo-parabolic problem is being considered. To solve this problem numerically, we construct higher order difference method for approximation to the considered problem and obtain the error estimate for its solution. Based on the method of energy estimate the fully discrete scheme is shown to be convergent of order four in space and of order two in time. Numerical example is presented. (C) 2017 Elsevier B.V. All rights reserved.
Numerical Solution of Singularly Perturbed Fredholm Integro-Differential Equations by Homogeneous Second Order Difference Method
(Elsevier, 2022) Durmaz, Muhammet Enes; Cakir, Musa; Amirali, Ilhame; Amiraliyev, Gabil M.
This work presents a computational approximate to solve singularly perturbed Fredholm integro-differential equation with the reduced second type Fredholm equation. This problem is discretized by a finite difference approximate, which generates second-order uniformly convergent numerical approximations to the solution. Parameter-uniform approximations are generated using Shishkin type meshes. The performance of the numerical scheme is tested which supports the effectiveness of the technique. (c) 2022 Elsevier B.V. All rights reserved.
Numerical Treatment of a Quasilinear Initial Value Problem With Boundary Layer
(Taylor & Francis Ltd, 2016) Cakir, Musa; Cimen, Erkan; Amirali, Ilhame; Amiraliyev, Gabil M.
The paper deals with the singularly perturbed quasilinear initial value problem exhibiting initial layer. First the nature of solution of differential problem before presenting method for its numerical solution is discussed. The numerical solution of the problem is performed with the use of a finite-fitted difference scheme on an appropriate piecewise uniform mesh (Shishkin-type mesh). An error analysis shows that the method is first-order convergent except for a logarithmic factor, in the discrete maximum norm, independently of the perturbation parameter. Finally, numerical results supporting the theory are presented.