Numerical Solution of Linear Volterra Integral Equation with Delay using Bernstein Polynomial

Adhraa M Muhammad,A M Ayal

doi:10.29333/iejme/5880

Abstract

Bernstein polynomial is one of the most valuable and attractive method used to develop numerical solution for several complex models because of its robustness to demonstrate approximation for anonymous equations. In this paper, Bernstein polynomial is proposed to present effective solution for the 2nd kind linear Volterra integral equations with delay. To evaluate proposed method, the experiments are contacted using two examples and it is obtained the validity and applicability of the proposed method.

Highlights

Several methods have been proposed for numerical solution of these equations (Mustafa & AL-Zubaidy, 2011), Bhatta and Bhatti (2006) presented numerical solution Kdv equation using linear and non-linear differential equation both partial and ordinary by modified Bernstein polynomials
A solution for Volterra integral equation of the first kind based on Bernstein polynomials
A robust proposed approach is explored for recruiting Bernstein polynomial to solve linear Volterra integral equation of 2nd kind with delay

Summary

Introduction

Approximate methods for solving numerically various classes of integral equations (Shihab & Mohammed Ali, 2015) are very rare.Several methods have been proposed for numerical solution of these equations (Mustafa & AL-Zubaidy, 2011), Bhatta and Bhatti (2006) presented numerical solution Kdv equation using linear and non-linear differential equation both partial and ordinary by modified Bernstein polynomials. Bhattacharya and Mandal (2008) used of Bernstein polynomials is numerical solution of Volterra integral equations. AL-Zawi (2011) used Bernstein polynomials for solving Volterra integral equation of the second kind. Alturk (2016) presented application of the Bernstein polynomial for solving Volterra integral equations with convolution kernels as well. Mohamadi et al (2017) introduced Bernstein multiscaling polynomial and application by solving Volterra integral equations. Approximate methods for solving numerically various classes of integral equations (Shihab & Mohammed Ali, 2015) are very rare. Bhattacharya and Mandal (2008) used of Bernstein polynomials is numerical solution of Volterra integral equations. AL-Zawi (2011) used Bernstein polynomials for solving Volterra integral equation of the second kind.

Results

Conclusion