Comparison Solutions Between Lie Group Method and Numerical Solution of (RK4) for Riccati Differential Equation
Applied and Computational Mathematics
Volume 5, Issue 2, April 2016, Pages: 64-72
Received: Feb. 17, 2016; Accepted: Mar. 25, 2016; Published: Apr. 15, 2016
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Authors
Sami H. Altoum, Department of Mathematics, University College of Qunfudha, Umm Alqura University, Makkah, KSA
Salih Y. Arbab, Engineering College, Albaha University, Albaha, KSA
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Abstract
This paper introduced Lie group method as a analytical method and then compared to RK4 and Euler forward method as a numerical method. In this paper the general Riccati equation is solved by symmetry group. Numerical comparisons between exact solution, Lie symmetry group and RK4 on these equations are given. In particular, some examples will be considered and the global error computed numerically.
Keywords
Riccati Equation, Symmetry Group, Infinitesimal Generator, Runge-Kutta
To cite this article
Sami H. Altoum, Salih Y. Arbab, Comparison Solutions Between Lie Group Method and Numerical Solution of (RK4) for Riccati Differential Equation, Applied and Computational Mathematics. Vol. 5, No. 2, 2016, pp. 64-72. doi: 10.11648/j.acm.20160502.15
Copyright
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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