The Combined Laplace-homotopy Analysis Method for Partial Differential Equations

Volume 16, Issue 1, pp 88-102 http://dx.doi.org/10.22436/jmcs.016.01.10

Publication Date: March 15, 2016 Submission Date: September 15, 2015

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Authors

Javad Vahidi - Department of Mathematics, Iran University of Science and Technology, Tehran, Iran.

Abstract

In this paper, the Laplace transform homotopy analysis method (LHAM) is employed to obtain approximate analytical solutions of the linear and nonlinear differential equations. This method is a combined form of the Laplace transform method and the homotopy analysis method. The proposed scheme finds the solutions without any discretization or restrictive assumptions and is free from round-off errors and therefore, reduces the numerical computations to a great extent. Some illustrative examples are presented and the numerical results show that the solutions of the LHAM are in good agreement with those obtained by exact solution.

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Keywords

• Homotopy analysis method
• Laplace transform method
• partial differential equation.

MSC

•  54A40
•  26E50

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