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Applications of Adaptive Multi Step Differential Transform Method to Singular Perturbation Problems Arising in Science and Engineering |
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PP: 223-232 |
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Author(s) |
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Essam R. El-Zahar,
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Abstract |
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| 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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