Numerical solution of time fractional nonlinear Schrodinger equation arising in quantum mechanics by cubic B-spline finite elements
Authors :
Alaattin Esena,* and Orkun Tasbozan b
Author Address :
aepartment of Mathematics, Faculty of Science and Art, In¨on¨u University, Malatya, 44280, TURKEY.
bDepartment of Mathematics, Faculty of Science and Art, Mustafa Kemal University, Hatay, 31000, TURKEY.
*Corresponding author.
Abstract :
In the present article, we are going to investigate the numerical solutions of time fractional nonlinear Schrodinger equation which is frequently encountered in quantum mechanics by using cubic B-spline collocation method. To be able to control the efficiency of the proposed method, some sample problems have been studied in this article. The outstanding purpose of the paper is to indicate that the finite element method based on the cubic B-spline collocation method approach can also be suitable for the handling of the fractional differential equations. At the end, the results of numerical experiments are compared with those of analytical solution to ensure the accuracy and efficiency of the presented scheme.
Keywords :
Finite element method, collocation method, time fractional nonlinear Schrodinger equation, cubic B-Spline, fractional quantum mechanics.
DOI :
Article Info :
Received : March 10, 2015; Accepted : August 23, 2015.
