eng
International Academy of Ecology and Environmental Sciences
Computational Ecology and Software
2220-721X
2015-12-1
5
4
380
388
10
article
A discrete homotopy perturbation method for non-linear Schrodinger
equation
H. A. Wahab
1
2
Khalid Usman
1
2
Muhammad Naeem
1
2
Sarfraz Ahmad
1
2
Saira Bhatti
1
2
Muhammad
Shahzad
1
2
Hazrat Ali
1
2
Department of Mathematics, Hazara University, Manshera, Pakistan
Department of IT, Abbottabad University of Science and Technology, Abbottabad, Pakistan
Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad, Pakistan
Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad, Pakistan
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.
http://www.iaees.org/publications/journals/ces/articles/2015-5(4)/discrete-homotopy-perturbation-method-for-non-linear-Schrodinger-equation.pdf
discrete homotopy perturbation method
nonlinear models
discretisation