Numerical solution of the Sturm-Liouville problem by using Chebyshev cardinal functions

Subject Areas : Statistics

M.  Shahriari ¹ (Department of Mathematics, Faculty of Science, University of Maragheh, P.O. Box 55181-83111, Maragheh, Iran)
B.  Nemati Saray ² (Faculty of Mathematics, Zanjan University of Basic Sciences, Zanjan, postcode, 45137-66731 Iran)
F.  Pashaie ³ (Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran)

Received: 2018-01-20 Accepted : 2018-09-24 Published : 2019-02-20

Keywords: مسأله اشتورم-لیوویل, چندجمله‌ای‌ چبیشف, تابع کاردینال چبیشف, ماتریس عملیاتی مشتق,

Abstract :

In this manuscript, a numerical technique is presented for finding the eigenvalues of the regular Sturm-Liouville problems. The Chebyshev cardinal functions are used to approximate the eigenvalues of a regular Sturm-Liouville problem with Dirichlet boundary conditions.These functions defined by the Chebyshev function of the first kind. By using the operational matrix of derivative the problem is reduced to a set of algebraic equation. Finally we use some numerical examples to show that this method include to demonstrate the validity and applicability of technique.

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