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01-Applied Mathematics & Information Sciences
An International Journal
               
 
 
 
 
 
 
 
 
 
 
 

Content
 

Volumes > Volume 9 > No. 1

 
   

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

PP: 223-232
Author(s)
Essam R. El-Zahar,
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.

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