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Computational Ecology and Software, 2015, 5(4): 380-388
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Article

A discrete homotopy perturbation method for non-linear Schrodinger equation

H. A. Wahab1, Khalid Usman1, Muhammad Naeem2, Sarfraz Ahmad3, Saira Bhatti4, Muhammad Shahzad1, Hazrat Ali1
1Department of Mathematics, Hazara University, Manshera, Pakistan
2Department of IT, Abbottabad University of Science and Technology, Abbottabad, Pakistan
3Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad, Pakistan
4Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad, Pakistan

Received 12 July 2015;Accepted 20 August 2015;Published online 1 December 2015
IAEES

Abstract
A general analysis is made by homotopy perturbation method while taking the advantages of the initial guess, appearance of the embedding parameter, different choices of the linear operator to the approximated solution to the non-linear Schrodinger equation. We are not dependent upon the Adomian polynomials and find the linear forms of the components without these calculations. The discretised forms of the nonlinear Schrodinger equation allow us whether to apply any numerical technique on the discritisation forms or proceed for perturbation solution of the problem. The discretised forms obtained by constructed homotopy provide the linear parts of the components of the solution series and hence a new discretised form is obtained. The general discretised form for the NLSE allows us to choose any initial guess and the solution in the closed form.

Keywords discrete homotopy perturbation method;nonlinear models;discretisation.



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