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.

In this paper we introduce the reproducing kernel method to solve a class of variational problems (VPs) depending on indefinite integrals. We discuss an analysis of convergence and error for the proposed method. Some test examples are presented to demonstrate the validity and applicability of method. The results of numerical examples indicate that the proposed method is computationally very simple and attractive.