Applications of Adaptive Multi Step Differential Transform Method to Singular Perturbation Problems Arising in Science and Engineering

Authors

Essam R. El-Zahar, Department of Mathematics, College of Sciences and Humanities, Salman bin Abdulaziz University, P. O. Box 83, Alkharj, 11942, Saudi Arabia\\ Department of Basic Engineering Science, Faculty of Engineering, Shebin El-Kom, Menofia University, EgyptFollow

Author Country (or Countries)

Egypt

Abstract

In this paper, piecewise-analytical and numerical solutions of singular perturbation initial-value problems are obtained by an adaptive multi-step differential transform method (MsDTM). The principle of the method is introduced, and then applied to different types of practical problems arising in science and engineering. Analytical and numerical solutions are obtained using piecewise convergent series with easily computable components over a sequence of variable-length sub-intervals. Numerical results are compared to those obtained by the classical MsDTM and the Runge-Kutta method. The results demonstrate the reliability and efficiency of the method in solving the considered problems.

Digital Object Identifier (DOI)

http://dx.doi.org/10.12785/amis/090128

Recommended Citation

R. El-Zahar, Essam (2015) "Applications of Adaptive Multi Step Differential Transform Method to Singular Perturbation Problems Arising in Science and Engineering," Applied Mathematics & Information Sciences: Vol. 09: Iss. 1, Article 35.
DOI: http://dx.doi.org/10.12785/amis/090128
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss1/35