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

Journal of Linear and Topological Algebra

مقاله 1، دوره 04، شماره 02، مرداد 2015، صفحه 87-100   

نوع مقاله: Research Paper

نویسندگان

A. Fallahzadeh^{* 1}؛ M. A. Fariborzi Araghi¹؛ V. Fallahzadeh²

¹Department of Mathematics, Islamic Azad University, Central Tehran Branch, PO. Code 14168-94351, Iran

²Department of Mathematics, Islamic Azad University, Arac Branch, Iran

چکیده

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

کلیدواژه‌ها

Homotopy Analysis Method؛ System of partial differential equations؛ H-surface

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