A second-order implicit difference scheme for the nonlinear time-space fractional Schrödinger equation

2020 ◽  
Vol 153 ◽  
pp. 399-411 ◽  
Author(s):  
Mingfa Fei ◽  
Nan Wang ◽  
Chengming Huang ◽  
Xiaohua Ma
Keyword(s):  
Schrödinger Equation ◽  
Difference Scheme ◽  
Schrodinger Equation ◽  
Second Order ◽  
Implicit Difference Scheme ◽  
Fractional Schrödinger Equation ◽  
Time Space ◽  
Fractional Schrodinger Equation

scholarly journals Modified Fractional Variational Iteration Method for Solving the Generalized Time-Space Fractional Schrödinger Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Baojian Hong ◽  
Dianchen Lu
Keyword(s):  
Schrödinger Equation ◽  
Iteration Method ◽  
Schrodinger Equation ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Fractional Schrödinger Equation ◽  
Variational Iteration ◽  
Time Space ◽  
Generalized Time ◽  
Fractional Schrodinger Equation

Based on He’s variational iteration method idea, we modified the fractional variational iteration method and applied it to construct some approximate solutions of the generalized time-space fractional Schrödinger equation (GFNLS). The fractional derivatives are described in the sense of Caputo. With the help of symbolic computation, some approximate solutions and their iterative structure of the GFNLS are investigated. Furthermore, the approximate iterative series and numerical results show that the modified fractional variational iteration method is powerful, reliable, and effective when compared with some classic traditional methods such as homotopy analysis method, homotopy perturbation method, adomian decomposition method, and variational iteration method in searching for approximate solutions of the Schrödinger equations.

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