A New Approach for Solving Volterra Integral Equations Using The Reproducing Kernel ‎Method

Subject Areas : International Journal of Industrial Mathematics

R. Ketabchi‎ ¹ , R. Mokhtari ² , E. Babolian ³

1 - Department of Mathematics, Science and Research branch, Islamic Azad University,Tehran,Iran.
2 - Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran.
3 - Department of Mathematics, Science and Research branch, Islamic Azad University, Tehran, Iran.

Received: 2016-11-18 Accepted : 2016-11-18 Published : 2017-11-01

Keywords: Reproducing kernel method, Volterra integral equations, Gram-Schmidt orthogonalization,

Abstract :

This paper is concerned with a technique for solving Volterra integral 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.