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

• Published in: Engineering analysis with boundary elements Vol. 32; no. 9; pp. 747 - 756
• Main Authors: Dehghan, Mehdi, Mirzaei, Davoud
• Format: Journal Article
• Language: English
• 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
• ISSN: 0955-7997; 1873-197X
• DOI: 10.1016/j.enganabound.2007.11.005

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...