Browsing by Author "Sevgin, Sebaheddin"

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An Approximation Property of Gaussian Functions
(Texas State Univ, 2013) Jung, Soon-Mo; Sevli, Hamdullah; Sevgin, Sebaheddin
Using the power series method, we solve the inhomogeneous linear first order differential equation y'(x) + lambda(x - mu)y(x) = Sigma(infinity)(m = 0) a(m) (x - mu)(m), and prove an approximation property of Gaussian functions.
Behavior of Solutions of Nonlinear Functional Volterra Integro-Differential Equations With Multiple Delays
(Dynamic Publishers, inc, 2016) Graef, John R.; Tunc, Cemil; Sevgin, Sebaheddin
The authors consider the nonlinear functional Volterra integro-differential equation with multiple delays x'(t) = -a(t)x(t) + Sigma(n)(i=1) integral(t)(t-tau i) b(i)(t,s)f(i)(x(s))ds. They give sufficient conditions so that solutions are bounded, belong to L-1, or belong to L-2. They also prove the stability and global asymptotic stability of the zero solution. Their technique of proof involves defining appropriate Lyapunov functionals.
Numerical Solution of a Singularly Perturbed Volterra Integro-Differential Equation
(Springer international Publishing Ag, 2014) Sevgin, Sebaheddin
We study the convergence properties of a difference scheme for singularly perturbed Volterra integro-differential equations on a graded mesh. We show that the scheme is first-order convergent in the discrete maximum norm, independently of the perturbation parameter. Numerical experiments are presented, which are in agreement with the theoretical results.
On the Perturbation of Volterra Integro-Differential Equations
(Pergamon-elsevier Science Ltd, 2013) Jung, Soon-Mo; Sevgin, Sebaheddin; Sevli, Hamdullah
In this work, we will prove that every solution of a perturbed Volterra integro-differential equation can be approximated by a solution of the Volterra integro-differential equation. (C) 2013 Elsevier Ltd. All rights reserved.
The Stability Analysis of The System of Integrodifferential Equations
(Univ Prishtines, 2024) Sevgin, Sebaheddin; Abdullah, Jargees Abdulwahid; Abdulazeez, Sadeq Taha
In this study, we use the fixed-point theorem of Margolis and Diaz to investigate the Ulam-Hyers-Rassias stability of a linear system of Volterra integrodifferential equations. We also extended this finding to a n-th order linear Volterra integrodifferential problem. In addition, we present examples to highlight the relevance of our findings. The discovered conclusions are theoretically significant and have possible applications in a variety of mathematical and scientific domains.
Uniform Difference Method for Singularly Perturbed Volterra Integro-Differential Equations
(Elsevier Science inc, 2006) Amiraliyev, G. M.; Sevgin, Sebaheddin
Singularly perturbed Volterra integro-differential equations is considered. An exponentially fitted difference scheme is constructed in a uniform mesh which gives first order uniform convergence in the discrete maximum norm. Numerical experiments support the theoretical results. (c) 2006 Elsevier Inc. All rights reserved.