Differential Transformation Method and Variation Iteration Method for Cauchy Reaction-diffusion Problems

Volume 1, Issue 2, pp 61--75 http://dx.doi.org/10.22436/jmcs.001.02.01

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Authors

Mohamed I. A. Othman - Department of Mathematics, Faculty of Science, Zagazig University, P. O. Box 44519, Zagazig, Egypt A. M. S. Mahdy - Department of Mathematics, Faculty of Science, Zagazig University, P. O. Box 44519, Zagazig, Egypt

Abstract

In this chapter, we will compare the differential transform method (DTM) and variational iteration method (VIM) for solving the one-dimensional, time dependent reaction-diffusion equations. Different cases of the equation are discussed and analytical solution in series form can be derived. The results obtained by the proposed method (DTM) are compared with the results obtained by (VIM). Some examples are presented to show the ability of the methods for such problems.

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Keywords

• Differential transformation
• Variation iteration method
• Cauchy reaction- diffusion problems
• Taylor’s series expansion.

MSC

•  35K57
•  41A58
•  65M99
•  65L99
•  65L05

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