Homotopy Analysis Laplace Transform Method for Analytical Solution of Porous Medium Equation


Authors : Dhara T. Patel; Amit K.Parikh

Volume/Issue : Volume 7 - 2022, Issue 11 - November

Google Scholar : https://bit.ly/3IIfn9N

Scribd : https://bit.ly/3OzOpWh

DOI : https://doi.org/10.5281/zenodo.7353208

Abstract : In the present paper, we have derived an analytical solution of a porous medium equation utilizing Homotopy Analysis Laplace Transform Method (HALTM). The suggested approach is an amalgamation of Homotopy Analysis Method and Laplace Transform Method. The analytical solutions have been obtained in terms of convergent series by proper choice of convergence control parameter. The results conclude that this method is extremely simple and efficient. This method is suitable for other nonlinear differential equations.

Keywords : Homotopy Analysis Method, Laplace Transformation, Porous medium equation.

In the present paper, we have derived an analytical solution of a porous medium equation utilizing Homotopy Analysis Laplace Transform Method (HALTM). The suggested approach is an amalgamation of Homotopy Analysis Method and Laplace Transform Method. The analytical solutions have been obtained in terms of convergent series by proper choice of convergence control parameter. The results conclude that this method is extremely simple and efficient. This method is suitable for other nonlinear differential equations.

Keywords : Homotopy Analysis Method, Laplace Transformation, Porous medium equation.

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