A computational method for solving periodic boundary value problems for integro-differential equations of Fredholm-Volterra type
Abstract In this paper, the numerical solution of periodic Fredholm–Volterra integro–differential equations of first-order is discussed in a reproducing kernel Hilbert space. A reproducing kernel Hilbert space is constructed, in which the periodic condition of the problem is satisfied. The exact solution u x is represented in the form of series in the space W 2 2 . In the mean time, the n-term approximate solution u n x is obtained and is proved to converge to the exact solution u x . Furthermore, we present an iterative method for obtaining the solution in the space W 2 2 . Some examples are displayed to demonstrate the validity and applicability of the proposed method. The numerical result indicates that the proposed method is straightforward to implement, efficient, and accurate for solving linear and nonlinear equations.