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Fully Discrete Galerkin Finite Element Method for the Cubic Nonlinear Schrödinger Equation

  • Jianyun Wang (a1) and Yunqing Huang (a2)
Abstract
Abstract

This paper is concerned with numerical method for a two-dimensional time-dependent cubic nonlinear Schrödinger equation. The approximations are obtained by the Galerkin finite element method in space in conjunction with the backward Euler method and the Crank-Nicolson method in time, respectively. We prove optimal L 2 error estimates for two fully discrete schemes by using elliptic projection operator. Finally, a numerical example is provided to verify our theoretical results.

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*Corresponding author. Email addresses: wjy8137@163.com (J. Y. Wang), huangyq@xtu.edu.cn (Y. Q. Huang)
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Numerical Mathematics: Theory, Methods and Applications
  • ISSN: 1004-8979
  • EISSN: 2079-7338
  • URL: /core/journals/numerical-mathematics-theory-methods-and-applications
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