Browsing by Author "Cimen, E."

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Explicit Finite Difference Methods for the Delay Pseudoparabolic Equations
(Hindawi Publishing Corporation, 2014) Amirali, I.; Amiraliyev, G. M.; Cakir, M.; Cimen, E.
Finite difference technique is applied to numerical solution of the initial-boundary value problem for the semilinear delay Sobolev or pseudoparabolic equation. By the method of integral identities two-level difference scheme is constructed. For the time integration the implicit rule is being used. Based on the method of energy estimates the fully discrete scheme is shown to be absolutely stable and convergent of order two in space and of order one in time. The error estimates are obtained in the discrete norm. Some numerical results confirming the expected behavior of the method are shown.
A Novel Uniform Numerical Approach To Solve a Singularly Perturbed Volterra Integro-Differential Equation
(Pleiades Publishing inc, 2023) Cakir, M.; Cimen, E.
In this paper, the initial value problem for the second order singularly perturbed Volterra integro-differential equation is considered. To solve this problem, a finite difference scheme is constructed, which based on the method of integral identities using interpolating quadrature rules with remainder terms in integral form. As a result of the error analysis, it is proved that the method is first-order convergent uniformly with respect to the perturbation parameter in the discrete maximum norm. Numerical experiments supporting the theoretical results are also presented.
A Uniform Numerical Method for Solving a Singularly Perturbed Neutral Delay Differential Equation
(Pleiades Publishing Ltd, 2025) Ekinci, Y.; Cimen, E.; Cakir, M.
In this paper, we deal with a singularly perturbed neutral-type delay differential problem. To solve this problem numerically, we construct a novel difference scheme on a layer-adapted mesh with the finite difference method by using interpolated quadrature rules with remainder terms in integral form. We prove that this scheme is first-order uniformly convergent with respect to the small perturbation parameter in discrete maximum norm. We also present numerical experiments which confirm the theoretical findings.