A Block by Block Method for Solving System of Volterra Integral Equations with Continuous and Abel Kernels

Abstract

The aim of the present paper is to introduce a block by block method for solving system of nonlinear Volterra integral equations with continuous kernels and system of Abel integral equations. We prove convergence of the method and show that its convergence order is at least six. To illustrate performance of the method, numerical experiments are presented and they are compared with HPM (Homotopy Perturbation Method) and RBFN (Radial Basis Function Network) method. The given results demonstrate remarkable ability of the proposed method.

Keywords:

• Abel integral equations
• Romberg quadrature rule
• block by block method
• nonlinear Volterra integral equations

AMS Subject Classification:

• 65R20