Volume 10, Issue 4
Fourth-Order Compact Split-Step Finite Difference Method for Solving the Two- and Three-Dimensional Nonlinear Schrödinger Equations

Rena Eskar, Xinlong Feng & Pengzhan Huang

Adv. Appl. Math. Mech., 10 (2018), pp. 879-895.

Published online: 2018-07

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  • Abstract

In this paper we show a fourth-order compact split-step finite difference method to solve the two- and three-dimensional nonlinear Schrödinger equations. The conservation properties and stability are analyzed for the proposed scheme. Numerical results show that the method can provide accurate and stable solutions for the nonlinear Schrödinger equation.

  • Keywords

Nonlinear Schrödinger equation, operator splitting method, compact split-step finite difference method, conservation law, stability.

  • AMS Subject Headings

65M15, 65Y20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-10-879, author = {Rena Eskar , and Xinlong Feng , and Huang , Pengzhan}, title = {Fourth-Order Compact Split-Step Finite Difference Method for Solving the Two- and Three-Dimensional Nonlinear Schrödinger Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {10}, number = {4}, pages = {879--895}, abstract = {

In this paper we show a fourth-order compact split-step finite difference method to solve the two- and three-dimensional nonlinear Schrödinger equations. The conservation properties and stability are analyzed for the proposed scheme. Numerical results show that the method can provide accurate and stable solutions for the nonlinear Schrödinger equation.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2017-0162}, url = {http://global-sci.org/intro/article_detail/aamm/12500.html} }
TY - JOUR T1 - Fourth-Order Compact Split-Step Finite Difference Method for Solving the Two- and Three-Dimensional Nonlinear Schrödinger Equations AU - Rena Eskar , AU - Xinlong Feng , AU - Huang , Pengzhan JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 879 EP - 895 PY - 2018 DA - 2018/07 SN - 10 DO - http://doi.org/10.4208/aamm.OA-2017-0162 UR - https://global-sci.org/intro/article_detail/aamm/12500.html KW - Nonlinear Schrödinger equation, operator splitting method, compact split-step finite difference method, conservation law, stability. AB -

In this paper we show a fourth-order compact split-step finite difference method to solve the two- and three-dimensional nonlinear Schrödinger equations. The conservation properties and stability are analyzed for the proposed scheme. Numerical results show that the method can provide accurate and stable solutions for the nonlinear Schrödinger equation.

Rena Eskar, Xinlong Feng & Pengzhan Huang. (2020). Fourth-Order Compact Split-Step Finite Difference Method for Solving the Two- and Three-Dimensional Nonlinear Schrödinger Equations. Advances in Applied Mathematics and Mechanics. 10 (4). 879-895. doi:10.4208/aamm.OA-2017-0162
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