Numerical solutions for the system of Fredholm integral equations of second kind by a new approach involving semiorthogonal B-spline wavelet collocation method

Abstract

In this paper, a new approach based on linear B-spline wavelet method has been developed to approximate the solutions of system of linear Fredholm integral equations of second kind. Compactly supported linear semi-orthogonal B-spline scaling functions and wavelet functions together with their dual functions are applied to approximate the solutions of linear Fredholm integral equations system of second kind. This method reduces the system of integral equations to a linear system of algebraic equations that can be solved easily with any of the usual methods. The numerical results obtained by the present method have been compared with those obtained by adaptive method based on Trapezoidal rule. Numerical examples are presented to illustrate the accuracy of the method.