IJPAM: Volume 105, No. 3 (2015)

ON THE EXPONENTIAL CHEBYSHEV APPROXIMATION
IN UNBOUNDED DOMAINS:
A COMPARISON STUDY FOR SOLVING
HIGH-ORDER ORDINARY DIFFERENTIAL EQUATIONS

M.A. Ramadan$^1$, K.R. Raslan$^2$, T.S. El Danaf$^3$, M.A. Abd El Salam$^4$
$^{1,3}$Mathematics Department
Faculty of Science
Menoufia University
Shebein El-Koom, EGYPT
$^{2,4}$Mathematics Department
Faculty of Science
Al-Azhar University
Nasr-City,11884, Cairo, EGYPT


Abstract. In this paper we investigate an improved scheme for exponential Chebyshev (EC) collocation method. The improved scheme of the EC functions is derived and introduced for solving high-order linear ordinary differential equations with variable coefficients in unbounded domain. This technique transforms the given differential equation and mixed conditions to matrix equation with unknown EC coefficients. These matrices together with the collocation method are utilized to reduce the solution of higher-order ordinary differential equations to the solution of a system of algebraic equations. The solution is obtained in terms of EC functions. Numerical examples are given to demonstrate the validity and applicability of the method. The obtained numerical results are compared with others existing methods and the exact solution where it shown to be very attractive with good accuracy.

Received: August 16, 2015

AMS Subject Classification: 65L20, 65L05, 65L10

Key Words and Phrases: exponential Chebyshev functions, higher-order ordinary differential equations, exponential Chebyshev collocation method

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DOI: 10.12732/ijpam.v105i3.8 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 105
Issue: 3
Pages: 399 - 413


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