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

Author

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  • Li, Xiaolin
  • Li, Shuling

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.

Suggested Citation

  • Li, Xiaolin & Li, Shuling, 2023. "Analysis of an element-free Galerkin method for the nonlinear Schrödinger equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 538-552.
    • Handle: RePEc:eee:matcom:v:203:y:2023:i:c:p:538-552
    DOI: 10.1016/j.matcom.2022.06.031
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