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 ⊕j=1n(W22[a,b]⊕W22[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 ⊕j=1n(W22[a,b]⊕W22[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.