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

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 W 2 3 [ a , b ] ⊕ W 2 . 3 [ a , b ] . The convergence of the method is proven and its exactness is illustrated by three numerical examples.