Volume 3, Issue 6, December 2014, Page: 315-322
An Approximate Analytical Solution of Higher-Order Linear Differential Equations with Variable Coefficients Using Improved Rational Chebyshev Collocation Method
Mohamed A. Ramadan, Mathematics Department, Faculty of Science, Menoufia University, Shebein El-Koom, Egypt
Kamal R. Raslan, Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, Egypt
Mahmoud A. Nassar, Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, Egypt
Received: Dec. 5, 2014;       Accepted: Dec. 18, 2014;       Published: Dec. 27, 2014
DOI: 10.11648/j.acm.20140306.15      View  1860      Downloads  154
Abstract
The purpose of this paper is to investigate the use of rational Chebyshev (RC) collocation method for solving high-order linear ordinary differential equations with variable coefficients. Using the rational Chebyshev collocation points, this method transforms the high-order linear ordinary differential equations and the given conditions to matrix equations with unknown rational Chebyshev 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 RC 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 and maintains better accuracy.
Keywords
Rational Chebyshev Functions, Higher-Order Ordinary Differential Equations, Rational Chebyshev Collocation Method
To cite this article
Mohamed A. Ramadan, Kamal R. Raslan, Mahmoud A. Nassar, An Approximate Analytical Solution of Higher-Order Linear Differential Equations with Variable Coefficients Using Improved Rational Chebyshev Collocation Method, Applied and Computational Mathematics. Vol. 3, No. 6, 2014, pp. 315-322. doi: 10.11648/j.acm.20140306.15
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