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.
| Published in | Applied and Computational Mathematics (Volume 5, Issue 2) |
| DOI | 10.11648/j.acm.20160502.15 |
| Page(s) | 64-72 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Riccati Equation, Symmetry Group, Infinitesimal Generator, Runge-Kutta
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APA Style
Sami H. Altoum, Salih Y. Arbab. (2016). Comparison Solutions Between Lie Group Method and Numerical Solution of (RK4) for Riccati Differential Equation. Applied and Computational Mathematics, 5(2), 64-72. https://doi.org/10.11648/j.acm.20160502.15
ACS Style
Sami H. Altoum; Salih Y. Arbab. Comparison Solutions Between Lie Group Method and Numerical Solution of (RK4) for Riccati Differential Equation. Appl. Comput. Math. 2016, 5(2), 64-72. doi: 10.11648/j.acm.20160502.15
AMA Style
Sami H. Altoum, Salih Y. Arbab. Comparison Solutions Between Lie Group Method and Numerical Solution of (RK4) for Riccati Differential Equation. Appl Comput Math. 2016;5(2):64-72. doi: 10.11648/j.acm.20160502.15
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Download@article{10.11648/j.acm.20160502.15,
author = {Sami H. Altoum and Salih Y. Arbab},
title = {Comparison Solutions Between Lie Group Method and Numerical Solution of (RK4) for Riccati Differential Equation},
journal = {Applied and Computational Mathematics},
volume = {5},
number = {2},
pages = {64-72},
doi = {10.11648/j.acm.20160502.15},
url = {https://doi.org/10.11648/j.acm.20160502.15},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20160502.15},
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.},
year = {2016}
}
TY - JOUR T1 - Comparison Solutions Between Lie Group Method and Numerical Solution of (RK4) for Riccati Differential Equation AU - Sami H. Altoum AU - Salih Y. Arbab Y1 - 2016/04/15 PY - 2016 N1 - https://doi.org/10.11648/j.acm.20160502.15 DO - 10.11648/j.acm.20160502.15 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 64 EP - 72 PB - Science Publishing Group SN - 2328-5613 UR - https://doi.org/10.11648/j.acm.20160502.15 AB - 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. VL - 5 IS - 2 ER -
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