The Approximate Solution of High-Order Nonlinear Ordinary Differential Equations by Improved Collocation Method with Terms of Shifted Chebyshev Polynomials

被引：0
作者：
Öztürk Y. [1 ]
Gülsu M. [2 ]
机构：
[1] Ula Ali Koçman Vocational School, Mugla Sıtkı Koçman University, Mugla
[2] Department of Mathematics, Faculty of Science, Mugla Sıtkı Koçman University, Mugla
来源：
International Journal of Applied and Computational Mathematics | 2016年 / 2卷 / 4期
关键词：
Collocation method; Lane–Emden equations; Nonlinear differential equation; Riccati equations; Shifted Chebyshev polynomial; Van der Pol equation;
D O I：
10.1007/s40819-015-0075-1
中图分类号：
学科分类号：
摘要：
In this paper, we present a direct computational method for solving the higher-order nonlinear differential equations by using collocation method. This method transforms the nonlinear differential equation into the system of nonlinear algebraic equations with unknown shifted Chebyshev coefficients, via Chebyshev–Gauss collocation points. The solution of this system yields the Chebyshev coefficients of the solution function. The method is valid for both initial-value and boundary-value problems. Several examples are presented to illustrate the accuracy and effectiveness of the method by the approximate solutions of very important equations of applied mathematics such as Lane–Emden equation, Riccati equation, Van der Pol equation. The approximate solutions can be very easily calculated using computer program Maple 13. © 2015, Springer India Pvt. Ltd.
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页码：519 / 531
页数：12
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