Numerical solution of linear Fredholm integral equations using sine–cosine wavelets

Abstract

If we divide the interval [0,1] into N sub-intervals, then sine–cosine wavelets on each sub-interval can approximate any function. This ability helps us to obtain a more accurate approximation of piecewise continuous functions, and, hence, we can obtain more accurate solutions of integral equations. In this article we use a combination of sine–cosine wavelets on the interval [0,1] to solve linear integral equations. We convert the integral equation into a system of linear equations. Numerical examples are given to demonstrate the applicability of the proposed method.

Keywords:

• Integral equations
• Sine–cosine wavelets
• Fourier functions
• Operational matrix
• Quadrature formulae