TY - JOUR
T1 - An Explicit Finite Difference Scheme for Solving the Space Fractional Nonlinear Schrödinger Equation
AU - Tang , Dongsheng
JO - Journal of Information and Computing Science
VL - 2
SP - 122
EP - 125
PY - 2024
DA - 2024/01
SN - 16
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jics/22370.html
KW - Partial Differential Equations, Finite difference method, Numerical solutions.
AB - <p style="text-align: justify;">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.</p>