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
Views 4734      Downloads 213
Sami H. Altoum, Department of Mathematics, University College of Qunfudha, Umm Alqura University, Makkah, KSA
Salih Y. Arbab, Engineering College, Albaha University, Albaha, KSA
Article Tools
Follow on us
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.
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 © 2016 Authors retain the copyright of this article.
This article 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.
W. T. Reid, Riccati Differential Equations (Mathematics in science and engineering), New York: Academic Press, 1972.
F. Dubois, A. Saidi, Unconditionally Stable Scheme for Riccati Equation, ESAIM Proceeding. 8(2000), 39-52.
A. A. Bahnasawi, M. A. El-Tawil and A. Abdel-Naby, Solving Riccati Equation using Adomians Decomposition Method, App. Math. Comput. 157(2007), 503-514.
T. Allahviraloo, Sh. S. Bahzadi. Application of Iterative Methods for Solving General Riccati Equation, Int. J. Industrial Mathematics, Vol. 4, ( 2012) No. 4, IJIM-00299.
Supriya Mukherjee, Banamali Roy. Solution of Riccati Equation with Variable Co-efficient by Differential Transform Method, Int. J. of Nonlinear Science Vol.14, (2012) No.2, pp. 251-256.
Taiwo, O. A., Osilagun J. A. Approximate Solution of Generalized Riccati Differential Equation by Iterative Decomposition Algorithm, International Journal of Engineering and Innivative Technology(IJEIT) Vol. 1(2012) No. 2, pp. 53-56.
J. Biazar, M. Eslami. Differential Transform Method for Quadratic Riccati Differential Equation, vol. 9 (2010) No.4, pp. 444-447.
Cristinel Mortici. The Method of the Variation of Constants for Riccati Equations, General Mathematics, Vol. 16(2008) No.1, pp. 111-116.
B. Gbadamosi, O. adebimpe, E. I. Akinola, I. A. I. Olopade. Solving Riccati Equation using Adomian Decomposition Method, International Journal of Pure and Applied Mathematics, Vol. 78(2012) No. 3, pp. 409-417.
Olever. P. J. Application of Lie Groups to Differential Equations. New York Springer-Verlag, (1993).
Al Fred Grany. Modern Differential Geometry of Curves and Surfaces, CRC Press, (1998).
Aubin Thierry. Differential Geometry, American Mathematical Society, (2001).
Nail. H. Ibragimov, Elementry Lie Group Analysis and Ordinary Differential Equations, John Wiley Sons New York, (1996).
T. R. Ramesh Rao, "The use of the A domain Decomposition Method for Solving Generalized Riccati Differential Equations" Proceedings of the 6th IMT-GT Conference on Mathematics, Statistics and its Applications (ICMSA2010) Universiti Tunku Abdul Rahman, Kuala Lumpur, Malaysia pp. 935-941.
B. Batiha, M. S. M. Noorani and I. Hashim, " Application of Variational Iteration Method to a General Riccati Equation" International Mathematical Forum, Vol.2, no. 56, pp. 2759–2770, 2007.
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
Tel: (001)347-983-5186