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Volume 16, Issue 2
An Explicit Finite Difference Scheme for Solving the Space Fractional Nonlinear Schrödinger Equation

Dongsheng Tang

J. Info. Comput. Sci. , 16 (2021), pp. 122-125.

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  • 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.

  • Keywords

Partial Differential Equations, Finite difference method, Numerical solutions.

  • AMS Subject Headings

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COPYRIGHT: © Global Science Press

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@Article{JICS-16-122, author = {Tang , Dongsheng}, title = {An Explicit Finite Difference Scheme for Solving the Space Fractional Nonlinear Schrödinger Equation}, journal = {Journal of Information and Computing Science}, year = {2021}, volume = {16}, number = {2}, pages = {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.

}, issn = {3080-180X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jics/22370.html} }
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 - 2021 DA - 2021/06 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 -

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.

Tang , Dongsheng. (2021). An Explicit Finite Difference Scheme for Solving the Space Fractional Nonlinear Schrödinger Equation. Journal of Information and Computing Science. 16 (2). 122-125. doi:
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