An Explicit Finite Difference Scheme for Solving the Space Fractional Nonlinear Schrödinger Equation
Year: 2021
Author: Dongsheng Tang
Journal of Information and Computing Science, Vol. 16 (2021), Iss. 2 : pp. 122–125
Abstract
This paper uses the finite difference method to numerically solve the space fractional nonlinear Schrodinger equation. First, we give some properties of the fractional Laplacian $Δ_h^\alpha.$ Then we construct a numerical scheme which satisfies the mass conservation law without proof and the scheme’s order is $o(\tau^2+h^2)$ in the discrete $L^\infty$ norm. Moreover, The scheme conserves the mass conservation and is unconditionally stable about the initial values. Finally, this article gives a numerical example to verify the relevant properties of the scheme.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2024-JICS-22370
Journal of Information and Computing Science, Vol. 16 (2021), Iss. 2 : pp. 122–125
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 4
Keywords: Partial Differential Equations Finite difference method Numerical solutions.