HAAR WAVELET COLLOCATION METHOD FOR SOLVING LINEAR VOLTERRA AND FREDHOLM INTEGRAL EQUATIONS

Abstract

The main purpose of this project is to obtain the numerical solution of linear volterra and fredholm integral equations by using Haar wavelet collocation method. Specifically, a numerical solution of the second kind of Linear volterra and fredholm integral equations has been discussed. This equation cannot be easily evaluated analytically. As a result, an efficient numerical technique has been applied to find the solution which is indeed an approximate solution. In this project, Haar wavelet collocation method is employed to find the approximate solution of linear volterra and fredholm integral equations. The Haar wavelet collocation method is utilized to convert this integral equation into a system of algebraic equations and the resulting system of algebraic equations are solved by using Gaussian elimination with partial pivoting to compute the Haar coefficients. The presented method is verified by means of different problems, where theoretical results are numerically confirmed. The numerical results of Eight test problems, for which the exact solutions are known, are considered to verify the accuracy and the efficiency of the proposed method. The numerical results are compared with the exact solutions and the performance of the Haar wavelet collocation method is demonstrated by calculating the error norm and maximum absolute errors for different number collocation points. The computational cost of the proposed methods is analyzed by examples and the error analysis is done by the Haar wavelet collocation method numerically. The convergence of the Haar wavelet collocation method is ensured at higher level resolution (J). The numerical results show that the method is applicable, accurate and efficient. Most of the computations are performed using MATLAB R2015a software.