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

الموضوعات : International Journal of Industrial Mathematics

M. A. Fariborzi Araghi ¹ , S. Naghshband ²

1 - Department of Mathematics, Islamic Azad University, Central Tehran Branch, P. O. Box 13185.768, Tehran, Iran.
2 - Department of Mathematics, Islamic Azad University, Central Tehran Branch, P. O. Box 13185.768, Tehran, Iran.

تاريخ الإرسال : 01 الإثنين , محرم, 1435 تاريخ التأكيد : 01 الإثنين , محرم, 1435 تاريخ الإصدار : 28 الأحد , محرم, 1435

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

ملخص المقالة :

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.