Weighted Residual Method for the System of Nonlinear Volterra Integral Equations of the Second Kind Using an Exponential Function

Chinar Sh Ahmed

doi:10.30526/34.3.2682

Abstract

The numerical resolve nonlinear system of Volterra integral equation of the second kind (NLSVIEK2) has been considered. The exponential function is used as the base function of the collocation method to approximate the resolve of the problem. Arithmetic epitome are performed which have already been solved by weighted residual manner, Taylor manner and block- by- block(2, 3, 5).

Highlights

IntroductionSolving the system of (linear and nonlinear) VIE of the second kind, many methods with enough accuracy and efficiency have already been used by many researches [1 - 9]
We use widened manner to approximate the resolve of the NLVIEK2 since one of its uses is to exchange intricate careers by some unpretentious careers so that integrated processes can be more unpretentious uttered
Resolve a System of Non-linear VIEK2 by a Collocation Manner: A collocation manner is based on approximating the resolve ( ), 1(1) by a partial sum 0 where ( ) naturally be choosing linearly independent

Summary

Introduction

Solving the system of (linear and nonlinear) VIE of the second kind, many methods with enough accuracy and efficiency have already been used by many researches [1 - 9]. We use widened manner to approximate the resolve of the NLVIEK2 since one of its uses is to exchange intricate careers by some unpretentious careers so that integrated processes can be more unpretentious uttered. A collocation manner (CM) has been used for solving integral and integro-differential equations by many authors and researchers [3, 5, 6, 8, 10, 11, 12, 13, 14, 15, 16, 17].

Resolve a System of Non-linear VIEK2 by a Collocation Manner:

Illustrative Epitome

Conclusion