A Computational Method for Nonlinear Fredholm Integro-Differential Equations Using Haar Wavelet Collocation Points

Abstract

Haar wavelet collocation points method is developed to the computational solution for nonlinear Fredholm integral and integro-differential equations on interval [0, tf ] using Leibnitz-Haar wavelet collocation points method. Essential principle is transmutation of the integral equation to equivalent higher order differential equation together with initial conditions. The transmutation is carried out using the Leibniz law. Haar wavelet collocation points and its operational matrix is employed to transform the higher order differential equation to a set of algebraic equations, then resolving these equations usage MATLAB program to calculate the demanded Haar coefficients. The computational results of the proposed approach is presented in four problems and make a simulation against the accurate solution. In addition, Error analysis is exhibited the proficiency of the proposed technique and when Haar wavelet resolutions increases the results are close to the accurate solutions.