We apologize for a recent technical issue with our email system, which temporarily affected account activations. Accounts have now been activated. Authors may proceed with paper submissions. PhDFocusTM
CFP last date
20 November 2024
Reseach Article

Article:A Simplified Derivation and Analysis of Fourth Order Runge Kutta Method

by Musa H., Ibrahim Saidu, M. Y. Waziri
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 9 - Number 8
Year of Publication: 2010
Authors: Musa H., Ibrahim Saidu, M. Y. Waziri
10.5120/1402-1891

Musa H., Ibrahim Saidu, M. Y. Waziri . Article:A Simplified Derivation and Analysis of Fourth Order Runge Kutta Method. International Journal of Computer Applications. 9, 8 ( November 2010), 51-55. DOI=10.5120/1402-1891

@article{ 10.5120/1402-1891,
author = { Musa H., Ibrahim Saidu, M. Y. Waziri },
title = { Article:A Simplified Derivation and Analysis of Fourth Order Runge Kutta Method },
journal = { International Journal of Computer Applications },
issue_date = { November 2010 },
volume = { 9 },
number = { 8 },
month = { November },
year = { 2010 },
issn = { 0975-8887 },
pages = { 51-55 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume9/number8/1402-1891/ },
doi = { 10.5120/1402-1891 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T19:58:06.105344+05:30
%A Musa H.
%A Ibrahim Saidu
%A M. Y. Waziri
%T Article:A Simplified Derivation and Analysis of Fourth Order Runge Kutta Method
%J International Journal of Computer Applications
%@ 0975-8887
%V 9
%N 8
%P 51-55
%D 2010
%I Foundation of Computer Science (FCS), NY, USA
Abstract

The derivation of fourth order Runge-Kutta method involves tedious computation of many unknowns and the detailed step by step derivation and analysis can hardly be found in many literatures. Due to the vital role played by the method in the field of computation and applied science/engineering, we simplify and further reduce the complexity of its derivation and analysis by exploring some possibly well-known works and propose a step by step derivation of the method. We have also shown the stability region graphically

References
  1. M.K. Jain, S.R.K. Iyengar, R.K. Jain, (2007), Numerical Methods for Scientific and Engineering Computing.
  2. J. D. Lambert, (1991), Numerical Methods for Ordinary Differential Systems, the initial value Problem, John Wiley & Sons Ltd.
  3. J.C. Butcher, (2003), Numerical Methods for Ordinary Differential Equations, John Wiley & Sons Ltd.
  4. John R. Dorman, (1996), Numerical Methods for Differential Equations, a Computational Approach, CRC Press, Inc.
  5. J. D. Lambert, (1973), Computational Methods in Ordinary Differential Equations, John Wiley & Sons Ltd
  6. Fudzia Ismail, (2010), Lecture Notes on Numerical Methods (unpublished), University Putra Malaysia
  7. G. Byrne and Hindmarsh, (1990), RK Methods prove popular at IMA Conference on Numerical ODE’s,SIAM News,23/2 pp.14-15.
  8. Lawrence F. Shampine, (1985),Interpolation for Runge-Kutta Methods.SIAM Journal of numerical analysis,22/5,pp.1014-1027.
Index Terms

Computer Science
Information Sciences

Keywords

Fourth order Runge Kutta Method Derivation Stability Analysis