A Numerical Method Based on RKHS for a Hyperbolic Initial-Boundary-Value Problem

Subject Areas : International Journal of Mathematical Modelling & Computations

Ebrahim Amini ^{1 *}

1 - Department of Mathematics, Payme Noor University, P. O. Box 19395-4697, Tehran, IRAN

Received: 2023-02-24 Accepted : 2023-09-16 Published : 2023-09-30

Keywords: Hyperbolic differential-integral equations, Initial and boundary conditions, Approximate solu-tion, Convergence analysis, Reproducing kernel Hilbert space,

Abstract :

The main aim of this article is to propose a computational method on the basis of the reproducing kernel Hilbert space method for solving a hyperbolic initial-boundary-value problem. The solution in reproducing kernel Hilbert space is constructed with series form, and the approximate solution vm is given as an m-term summation. Furthermore, convergence of the proposed method is presented which provides the theoretical basis of the proposed method. Finally, some numerical experiments are considered to demonstrate the efficiency and applicability of proposed method.

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