Numerical Simulation of Non-Linear Schrödinger Equations in Arbitrary Domain by the Localized Method of Approximate Particular Solution
Year: 2019
Author: Yongxing Hong, Jun Lu, Ji Lin, Wen Chen
Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 1 : pp. 108–131
Abstract
The aim of this paper is to propose a fast meshless numerical scheme for the simulation of non-linear Schrödinger equations. In the proposed scheme, the implicit-Euler scheme is used for the temporal discretization and the localized method of approximate particular solution (LMAPS) is utilized for the spatial discretization. The multiple-scale technique is introduced to obtain the shape parameters of the multi-quadric radial basis function for 2D problems and the Gaussian radial basis function for 3D problems. Six numerical examples are carried out to verify the accuracy and efficiency of the proposed scheme. Compared with well-known techniques, numerical results illustrate that the proposed scheme is of merits being easy-to-program, high accuracy, and rapid convergence even for long-term problems. These results also indicate that the proposed scheme has great potential in large scale problems and real-world applications.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2018-0026
Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 1 : pp. 108–131
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Schrödinger equation localized method of approximate particular solution shape parameters multiple-scale technique.
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