On the convergence of the homotopy analysis method to solve the system of partial differential equations

Subject Areas : Partial differential equations

A.  Fallahzadeh ¹ (Department of Mathematics, Islamic Azad University, Central Tehran Branch, PO. Code 14168-94351, Iran)
M. A.  Fariborzi Araghi ² (Department of Mathematics, Islamic Azad University, Central Tehran Branch, PO. Code 14168-94351, Iran)
V.  Fallahzadeh ³ (Department of Mathematics, Islamic Azad University, Arac Branch, Iran)

Received: 2015-06-12 Accepted : 2015-10-20 Published : 2015-05-01

Keywords: Homotopy Analysis Method, System of partial differential equations, H-surface,

Abstract :

One of the efficient and powerful schemes to solve linear and nonlinear equationsis homotopy analysis method (HAM). In this work, we obtain the approximate solution ofa system of partial differential equations (PDEs) by means of HAM. For this purpose, wedevelop the concept of HAM for a system of PDEs as a matrix form. Then, we prove theconvergence theorem and apply the proposed method to defined the approximate solution ofsome systems of PDEs. Also, we show the region of convergence by plotting the H-surface.

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