Numerical Solution of Nonlinear Volterra-Fredholm Integral Equations Using Haar Wavelet Collocation Method

S.C Shiralashetti,R.A Mundewadi

doi:10.18052/www.scipress.com/bmsa.18.50

S.C Shiralashetti, R.A Mundewadi

https://doi.org/10.18052/www.scipress.com/bmsa.18.50

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Abstract

In this paper, we present a numerical solution of nonlinear Volterra-Fredholm integral equations using Haar wavelet collocation method. Properties of Haar wavelet and its operational matrices are utilized to convert the integral equation into a system of algebraic equations, solving these equations using MATLAB to compute the Haar coefficients. The numerical results are compared with exact and existing method through error analysis, which shows the efficiency of the technique.

Highlights

Integral equations have motivated a large amount of research work in recent years
Since 1991 the various types of wavelet method have been applied for the numerical solution of different kinds of integral equations
Haar wavelet method is applied for different kind of integral equations, which among Lepik et al [29,30,31,32] presented the solution for differential and integral equations

Summary

Introduction

Integral equations have motivated a large amount of research work in recent years. Integral equations find its applications in various fields of mathematics, science and technology has been studied extensively both at the theoretical and practical level. Since 1991 the various types of wavelet method have been applied for the numerical solution of different kinds of integral equations. Haar wavelet method is applied for different type of problems. Shiralashetti et al [28] have introduced the adaptive gird Haar wavelet collocation method for the numerical solution of parabolic partial differential equations. Haar wavelet method is applied for different kind of integral equations, which among Lepik et al [29,30,31,32] presented the solution for differential and integral equations. Babolian et al [33] and Shiralashetti et al [34] applied for solving nonlinear Fredholm integral equations. We applied the Haar wavelet collocation method for the numerical solution of nonlinear Volterra-Fredholm integral equations.

Haar Wavelets

Method of Solution

Illustrative Examples

Conclusion