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### A Comparative Study of Homotopy Perturbation Method with Differential Transformation Method to Solve a Reaction Diffusion Equation

#### Affiliations

• Department of Mathematics, K. R. Mangalam University, Gurgaon-122103, Haryana, India

#### Abstract

In this paper, the solution of Cauchy problems for the reaction–diffusion equations are obtained using the as two well-known methods. The first method is He’s Homotopy Perturbation Method (HPM) and other method is Differential Transformation Method (DTM). To explain the capability and reliability of the methods, some cases have been defined. The proper implementation of He’s homotopy perturbation method can awfully lessen the size of work if compared with the standing differential transformation method. Comparisons of the results obtained by the homotopy perturbation method and differential transformation method several examples are provided. The results obtained using HPM and DTM are same results obtain by variational iteration method and MATLAB solution and then the capability of each method are also discussed.

#### Keywords

Cauchy Reaction-diffusion Equation, Differential Transformation Method, Homotopy Perturbation Method, MATLAB, Variational Iteration Method

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#### References

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