Analysis of an element-free Galerkin method for the nonlinear Schrödinger equation

Xiaolin Li and Shuling Li

Mathematics and Computers in Simulation (MATCOM), 2023, vol. 203, issue C, 538-552

Abstract: An element-free Galerkin method (EFGM) is proposed for meshfree numerical analysis of the nonlinear Schrödinger equation. In this method, an explicit linearized scheme with second-order time convergence is proposed to handle the nonlinearity, then the EFGM is used to obtain the discretize linear algebraic equations. The stability of the linearized scheme and the error of the EFGM are analyzed theoretically. Numerical experiments are presented to validate the effectiveness and theoretical analysis of the method.

Keywords: Meshless methods; Element-free Galerkin method; Time-dependent Schrödinger equation; Error splitting technique; Error estimate (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:203:y:2023:i:c:p:538-552

DOI: 10.1016/j.matcom.2022.06.031

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