Research Article Open Access

A Comparison of Explicit Semi-Analytical Numerical Integration Methods for Solving Stiff ODE Systems

E.R. El-Zahar1, H.M. Habib1, M.M. Rashidi2 and I.M. El-Desoky3
  • 1 Salman Bin Abdulaziz University, Saudi Arabia
  • 2 Menofia University, Egypt
  • 3 Tongji University, China
American Journal of Applied Sciences
Volume 12 No. 5, 2015, 304-320

DOI: https://doi.org/10.3844/ajassp.2015.304.320

Submitted On: 15 March 2015 Published On: 26 June 2015

How to Cite: El-Zahar, E., Habib, H., Rashidi, M. & El-Desoky, I. (2015). A Comparison of Explicit Semi-Analytical Numerical Integration Methods for Solving Stiff ODE Systems. American Journal of Applied Sciences, 12(5), 304-320. https://doi.org/10.3844/ajassp.2015.304.320

Abstract

In this study, a comparison among three semi-analytical numerical integration algorithms for solving stiff ODE systems is presented. The algorithms are based on Differential Transform Method (DTM) which are Multiple-Step DTM (MsDTM), Enhanced MsDTM (E-MsDTM) and MsDTM with Padé approximants (MsDTM-P). These methods can be classified as explicit one step semi-analytical numerical integration methods. The error and stability analysis of each method is presented. New important relationships among the methods are introduced. To demonstrate our results, a comparison of the accuracy, stability and computational efficiency of the methods is presented through solving some linear and nonlinear problems arising in applied science and engineering.

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Keywords

  • Multiple-Step Differential Transform Methods (MsDTM)
  • Enhanced MsDTM
  • Padé Approximants
  • Stiff Problems
  • Accuracy
  • Stability