Analytical solutions of first-order, periodic boundary value problem

Abstract

In this paper, the reproducing kernel method is applied to solve firstorder, periodic boundary value problems of Volterra integrodifferential equations. The analytical solution is represented in the form of convergent series with easily computable components. The solution methodology is based on generating the orthogonal basis from the obtained kernel function in the space W 2 2 [0, 1]. The n-term approximation is obtained and proved to converge to the analytical solution. Numerical examples are given to demonstrate the computation efficiency of the presented method. Results obtained by the method is very simple and effective.