The meshless local Petrov–Galerkin (MLPG) method for the generalized two-dimensional non-linear Schrödinger equation

In this paper the meshless local Petrov–Galerkin (MLPG) method is presented for the numerical solution of the two-dimensional non-linear Schrödinger equation. The method is based on the local weak form and the moving least squares (MLS) approximation. For the MLS, nodal points spread over the analyz...

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Bibliographic Details
Published inEngineering analysis with boundary elements Vol. 32; no. 9; pp. 747 - 756
Main Authors Dehghan, Mehdi, Mirzaei, Davoud
Format Journal Article
LanguageEnglish
Published Oxford Elsevier Ltd 01.09.2008
Elsevier
Subjects
Approximation
Boundary-integral methods
Computational techniques
Exact sciences and technology
Finite element method
Fundamental areas of phenomenology (including applications)
Mathematical analysis
Mathematical methods in physics
Mathematical models
Meshless local Petrov–Galerkin (MLPG) method
Meshless methods
Moving least square (MLS) approximation
Non-linear Schrödinger equation
Nonlinearity
Physics
Schroedinger equation
Two dimensional
Unit Heaviside test function
Unit Heaviside test function
Moving least square (MLS) approximation
Non-linear Schrödinger equation
Meshless local Petrov–Galerkin (MLPG) method
Predictor-corrector methods
Step method
Galerkin-Petrov method
Weak solution
Meshless method
Convergence rate
Schroedinger equation
Modelling
Non linear effect
Least square fit
Meshless local Petrov-Galerkin (MLPG) method
Numerical convergence
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Summary:In this paper the meshless local Petrov–Galerkin (MLPG) method is presented for the numerical solution of the two-dimensional non-linear Schrödinger equation. The method is based on the local weak form and the moving least squares (MLS) approximation. For the MLS, nodal points spread over the analyzed domain are utilized to approximate the interior and boundary variables. A time stepping method is employed for the time derivative. To deal with the non-linearity, we use a predictor–corrector method. A very simple and efficient method is presented for evaluation the local domain integrals. Finally numerical results are presented for some examples to demonstrate the accuracy, efficiency and high rate of convergence of this method.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0955-7997
1873-197X
DOI:10.1016/j.enganabound.2007.11.005