# The Combined Laplace-homotopy Analysis Method for Partial Differential Equations

Volume 16, Issue 1, pp 88-102 Publication Date: March 15, 2016       Article History
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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.

### Keywords

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

•  54A40
•  26E50

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