Soft Computing Technique for a System of Fuzzy Volterra Integro-Differential Equations in a Hilbert Space

Abstract

In this article, we implement a relatively new computational technique, a reproducing kernel Hilbert space method, for solving a system of fuzzy Volterra integro-differential equations in the Hilbert space circle plus(n)(j=1) (W-2(2) [a, b] circle plus W-2(2) [a, b]). Based on the concept of the reproducing kernel function combined with Gram-Schmidt orthogonalization process, we represent an exact solution in a form of Fourier series in the reproducing kernel Hilbert space circle plus(n)(j=1) (W-2(2) [a, b] circle plus W-2(2) [a, b]). Accordingly, the approximate solution of the system of fuzzy Volterra integro-differential equations is obtained by the n-term intercept of the exact solution and proved to converge to the exact solution. Finally, two numerical examples are presented to illustrate the reliability, appropriateness and efficiency of the method. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.