Solving system of Euler's equations using Runge –Kutta methods | ||
| Journal of University of Anbar for Pure Science | ||
| Article 35, Volume 17, Issue 2, December 2023, Pages 265-268 PDF (725.19 K) | ||
| Document Type: Research Paper | ||
| DOI: 10.37652/juaps.2023.181576 | ||
| Authors | ||
| Aseel Ali Al_Ameely* 1; Athraa N . Albukhuttar2 | ||
| 1Department of Mathematics, College of Education for Girls, University of Al-Kufa, Najaf – Iraq | ||
| 2Department of Mathematics, College of Education for Girls, University of Al-Kufa, Najaf , Iraq; | ||
| Abstract | ||
| In this paper, linear systems with variable coefficients (Euler's equations) were solved using one of the numerical methods that are subject to initial conditions defined over a given period of time .The explicit Rung-Kutta method is the fastest and most common numerical method starting with an initial value, the Rung-Kutta second order and Rung-Kutta fourth order. Analytical solutions of systems (systems with variable coefficients and systems with constant coefficients) were compared with the results of approximate solutions of the numerical method (Rung-Kutta second order And fourth order) and find out the accuracy of the results obtained for this approximate method after applying the Rung-Kutta algorithms performed with the Matlab program and finding the ratio of relative error between the exact and approximate solutions of the numerical method used, as well as solving a number of linear systems of Euler's equations of the first order supporting your results. | ||
| Keywords | ||
| Rung- kutta method; approximate solution; Systems of Euler equations | ||
|
Supplementary Files
|
||
| References | ||
|
[1] Athraa N ALbukhuttar, Hayder N kadhim andHussein A ALMasoudi, Application of Linear Equation Systems in Banking Auditing, 2nd International Conference on Physics and Applied Sciences (ICPAS 2021).
[2] Endre SMa𝒴er D. F., An introduction to Numerical Anal𝒴sis, Cambridge Universit𝒴 Press, 2003.
[3] J. D. Lambert, Numerical Methods for Ordinar𝒴 Differential S𝒴stems, The Initial Value Problem, John Wile𝒴 & Sons, London, UK, 1991.
[4] J. H. Verner, Some Runge-Kutta formula pairs, SIAM J. Numer. Anal., 28 (1991), pp. 496
Hayder N Kadhim,Athraa N Albukhuttar and Maha S Alibrahimi,The Use Of Mathematical Systems in Cost Accounting, AIP Conference Proceedings 2414 (1), 040087, 2023.
[6] Kasim Hussain, Fudziah Ismail, and Norazak Senu, Runge-Kutta T𝒴pe Methods for Directl𝒴 Solving Special Fourth-Order Ordinar𝒴 Differential Equations, Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2015, Article ID 893763.
[7] Mehmet Sezer, A𝒴şegülAk𝒴üz-Daşcıogˇlu , A Ta𝒴lor method for numerical solution of generalized pantograph equations with linear functional argument , Journal of Computational and Applied Mathematics 200 (1) , 2007.
[8] M.B. Canzonei, R. E. Cumb𝒴 and B.T. Diba, "Euler Equations and Mone𝒴 Market Interest Rate A Challenge for Monetar𝒴 Polic𝒴 Models", Georgetown Universit𝒴 ,Ma𝒴 ,2002.
[9] Tracogna S., Jackiewicz, A General Class of Two Step Runge-Kutta Method for ODEs, Springer Series in Computational Mathematics, Verlang 2010, 10(4).
[10] Taiwo O. A., Jimoh A. K., Bello A. K., Comparison of some Numerical Methods for the Solution of First and Second Orders Linear Integro Differential Equations, American Journal Of Engineering Research (AJER), 2014, 3(1). | ||
|
Statistics Article View: 62 PDF Download: 62 |
||
