On convergence of homotopy analysis method to solve the Schrodinger equation with a power law nonlinearity

Subject Areas : International Journal of Industrial Mathematics

M. A.  Fariborzi Araghi ¹ (Department of Mathematics, Islamic Azad University, Central Tehran Branch, P. O. Box 13185.768, Tehran, Iran.)
S.  Naghshband ² (Department of Mathematics, Islamic Azad University, Central Tehran Branch, P. O. Box 13185.768, Tehran, Iran.)

Received: 2013-11-04 Accepted : 2013-11-04 Published : 2013-12-01

Keywords: Schrodinger equation, Power law nonlinearity, Homotopy analysis method (HAM), Convergence,

Abstract :

In this paper, the homotopy analysis method (HAM) is considered to obtain the solution of the Schrodinger equation with a power law nonlinearity. For this purpose, a theorem is proved to show the convergence of the series solution obtained from the proposed method. Also, an example is solved to illustrate the eciency of the mentioned algorithm and theh-curve is plotted to determine the region of convergence.