Cardinal functions for Legendre pseudo-spectral method for solving the integro-differential equations

Khader, M.M.; Sweilam, N.H.; Kota, W.Y.

Cardinal functions for Legendre pseudo-spectral method for solving the integro-differential equations

Document Type : Original Article

Authors

¹ Department of Mathematics and Statistics, College of Science, Al-Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11566, Saudi Arabia

² Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt

³ Department of Mathematics, Faculty of Science, Damietta University, Damietta, Egypt

Abstract

In this article, we present a new numerical method to solve the integro-differential equations
(IDEs). The proposed method uses the Legendre cardinal functions to express the approximate
solution as a finite series. In our method the operational matrix of derivatives is used to
reduce IDEs to a system of algebraic equations. To demonstrate the validity and applicability of
the proposed method, we present some numerical examples. We compare the obtained numerical results from the proposed method with some other methods. The results show that the proposed algorithm is of high accuracy, more simple and effective.

Keywords