Application of reproducing kernel Hilbert space method for solving second-order fuzzy Volterra integro-differential equations

Abstract

Abstract In this article, we propose a new method that determines an efficient numerical procedure for solving second-order fuzzy Volterra integro-differential equations in a Hilbert space. This method illustrates the ability of the reproducing kernel concept of the Hilbert space to approximate the solutions of second-order fuzzy Volterra integro-differential equations. Additionally, we discuss and derive the exact and approximate solutions in the form of Fourier series with effortlessly computable terms in the reproducing kernel Hilbert space W23[a,b]⊕W2.3[a,b] $W_{2}^{3} [ a,b ] \oplus W_{2}^{.3} [ a,b ]$. The convergence of the method is proven and its exactness is illustrated by three numerical examples.

Keywords

• Reproducing kernel Hilbert space
• Complete orthonormal system
• Fuzzy Volterra integro-differential equation