Lucas Polynomial Approach for System of High-Order Linear Differential Equations and Residual Error EstimationReport as inadecuate




Lucas Polynomial Approach for System of High-Order Linear Differential Equations and Residual Error Estimation - Download this document for free, or read online. Document in PDF available to download.

Mathematical Problems in Engineering - Volume 2015 2015, Article ID 625984, 14 pages -

Research Article

Department of Mathematics, Faculty of Science, Celal Bayar University, Manisa, Turkey

Department of Mathematical Engineering, Faculty of Chemistry-Metallurgical, Yıldız Technical University, Istanbul, Turkey

Received 15 November 2014; Accepted 5 January 2015

Academic Editor: Mingshu Peng

Copyright © 2015 Muhammed Çetin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

An approximation method based on Lucas polynomials is presented for the solution of the system of high-order linear differential equations with variable coefficients under the mixed conditions. This method transforms the system of ordinary differential equations ODEs to the linear algebraic equations system by expanding the approximate solutions in terms of the Lucas polynomials with unknown coefficients and by using the matrix operations and collocation points. In addition, the error analysis based on residual function is developed for present method. To demonstrate the efficiency and accuracy of the method, numerical examples are given with the help of computer programmes written in Maple and Matlab.





Author: Muhammed Çetin, Mehmet Sezer, and Coşkun Güler

Source: https://www.hindawi.com/



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