Numerical solution of a linear Volterra integro-differential problem

Abstract

In this paper we develop an approximation method for numerically solving a linear Volterra integro-differential problem. The proposed method is based on a functional minimization problem in a finite-dimensional space generated by a finite Wendland’s type radial basis functions (RBFs) set. The existence and uniqueness of the solution are established and some convergence results are proved. Finally we present some numerical examples to show the effectiveness of this discrete method.