Research Article Open Access

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

E.R. El-Zahar1, H.M. Habib2, M.M. Rashidi3 and I.M. El-Desoky4
  • 1 Mathematics Department, Sciences and Humanities College, Salman bin Abdulaziz University, Alkharj, 11942, Saudi Arabia
  • 2 Basic Engineering Science Department, Engineering Faculty, Shebin El-Kom, Menofia University, Saudi Arabia
  • 3 Shanghai Automotive Wind Tunnel Center, Tongji University, Jiading, Shanghai 201804, Egypt
  • 4 Basic Engineering Science Department, Engineering Faculty, Shebin El-Kom, Menofia University, China

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.

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

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Keywords

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