A new reproducing kernel method for solving Volterra integro-dierential equations

Subject Areas : Applied Mathematics

Razieh Ketabchi ¹

1 - Department of Mathematics, Mobarakeh Branch, Islamic Azad University, Esfahan, Iran

Received: 2017-08-10 Accepted : 2017-10-28 Published : 2019-12-01

Keywords: Reproducing kernel method, integro-differential equations, Gram-Schmidt orthogonalization process,

Abstract :

This paper is concerned with a technique for solving Volterra integro-dierential equationsin the reproducing kernel Hilbert space. In contrast with the conventional reproducing kernelmethod, 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 toobtain the approximate solution. The convergence analysis is established theoretically. Theapplicability of the iterative method is demonstrated by testing some various examples.