Fourth Order Block-by-block Method to Solve System of Non-linear Volterra Integral Equations of the Second Kind

Borhan F Jumaa

doi:10.32894/kujss.2008.42088

Abstract

Fourth Order Block-by-block Method to Solve System of Non-linear Volterra Integral Equations of the Second Kind

Highlights

A block method is a class of self-starting methods which produce a block of values at a time (Delves & Mohamed, 1985).Second order blockby-block is described, modified, and used to solve Volterra integral equations of the second kind by (Linz, 1967)
The approaches of fourth order block-by-block method is applied for the first time to find the numerical solution for a NSVIEK2 (Jumaa, 2005) which is defined by: x
According to the numerical results which obtaining from the illustrative examples, we conclude that the method of fourth order block-by-block given the good results

Summary

Introduction

A block method is a class of self-starting methods which produce a block of values at a time (Delves & Mohamed, 1985).Second order blockby-block is described, modified, and used to solve Volterra integral equations of the second kind by (Linz, 1967). (AL-Asdi, 2002) used second and third order block-by-block for solving Hammersetien Volterra integral equations of the second kind, while (Saify, 2005) used second, third and fourth order block-by-block method for solving a system of linear. Volterra integral equation of the second kind, and (Ahmed, 2007) used second and third order block-by-block method for solving a system of nonlinear Volterra integral equation of the second kind. The approaches of fourth order block-by-block method is applied for the first time to find the numerical solution for a NSVIEK2 (Jumaa, 2005) which is defined by: x.

Then the Newton iterates are

Illustrative Examples

Exact solution

Conclusions