Cardinal functions for Legendre pseudo-spectral method for solving the integro-differential equations | ||||
| Journal of the Egyptian Mathematical Society | ||||
| Volume 22, Issue 3, October 2014, Page 511-516 PDF (625.45 K) | ||||
| Document Type: Original Article | ||||
 View on SCiNiTO | ||||
| Authors | ||||
| M.M. Khader1; N.H. Sweilam2; W.Y. Kota3 | ||||
| 1Department of Mathematics and Statistics, College of Science, Al-Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11566, Saudi Arabia | ||||
| 2Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt | ||||
| 3Department 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 | ||||
| Legendre cardinal functions; Integro-differential equations; Operational matrix method | ||||
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