Browsing by Author "Erdogan, F."

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A Hybrid Method for Singularly Perturbed Convection–diffusion Equation
(Springer, 2019) Sakar, M.G.; Saldır, O.; Erdogan, F.
In this research, we present a hybrid method which combination of simplified reproducing kernel method (SRKM) and asymptotic expansion for solving singularly perturbed convection–diffusion problems. According to the hybrid method, firstly asymptotic expansion formed on boundary layer domain and then terminal value problem solved via SRKM on regular domain. To apply the SRKM, some special Hilbert spaces are defined and related reproducing kernel functions are given. Then, the approximate solution is obtained as serial form. A new algorithm of SRKM is presented for nonlinear problem. Also, convergence analysis of approximate solution is given. Some linear and nonlinear problems are solved by hybrid method. The obtained outcomes indicate that the hybrid method is reliable and very effective for solving singularly perturbed convection–diffusion equation. © 2019, Springer Nature India Private Limited.
On the Instability of Solutions of Certain Non-Autonomous Vector Differential Equations of Fifth Order
(2007) Tunç, C.; Erdogan, F.
By using Lyapunov's function approach [13], some new results were established, which guarantee that the zero solution of non-linear vector differential equations of the form is unstable.
Solving a Class of Auto-Convolution Volterra Integral Equations Via Differential Transform Method
(University of Guilan, 2025) Tari, A.; Shahmorad, S.; Mostafazadeh, M.; Erdogan, F.
The aim of this paper is to solve a class of auto-convolution Volterra integral equations by the well-known differential transform method. The analytic property of solution and convergence of the method under some assumptions are discussed and some illustrative examples are given to clarify the theoretical results, accuracy and performance of the proposed method. © 2025 University of Guilan.
A Uniform Numerical Method for Dealing With a Singularly Perturbed Delay Initial Value Problem
(Pergamon-elsevier Science Ltd, 2010) Amiraliyeva, I. G.; Erdogan, F.; Amiraliyev, G. M.
This work deals with a singularly perturbed initial value problem fora quasi-linear second-order delay differential equation. An exponentially fitted difference scheme is constructed, in an equidistant mesh, which gives first-order uniform convergence in the discrete maximum norm. Numerical results are also presented. (C) 2010 Elsevier Ltd. All rights reserved.
Uniform Numerical Method for Singularly Perturbed Delay Differential Equations
(Pergamon-elsevier Science Ltd, 2007) Amiraliyev, G. M.; Erdogan, F.
This paper deals with the singularly perturbed initial value problem for a linear first-order delay differential equation. A numerical method is constructed for this problem which involves an appropriate piecewise-uniform mesh on each time subinterval. The difference scheme is shown to converge to the continuous solution uniformly with respect to the perturbation parameter. Numerical results are presented. (c) 2007 Elsevier Ltd. All rights reserved.