A new approach for solving Fredholm integro-differential equations using the reproducing kernel method

This paper is concerned with a technique for solving Fredholm integro-differential equations in the reproducing kernel Hilbert space. In contrast with the conventional reproducing kernel method, the Gram-Schmidt process is omitted here and satisfactory results are obtained. The analytical solution is represented in the form of series. An iterative method is given to obtain the approximate solution. The convergence analysis is established theoretically. The applicability of the iterative method is demonstrated by testing some various examples.