Stability and Convergence Analysis of Multi-Symplectic Variational Integrator for Nonlinear Schrödinger Equation

Siqi Lv, Zhihua Nie and Cuicui Liao ()
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Siqi Lv: Department of Information and Computing Science, College of Science, Jiangnan University, Wuxi 214122, China
Zhihua Nie: Jiangxi Institute of Intelligent Industry Technology Innovation, Nanchang 330052, China
Cuicui Liao: Department of Information and Computing Science, College of Science, Jiangnan University, Wuxi 214122, China

Mathematics, 2023, vol. 11, issue 17, 1-18

Abstract: Stability and convergence analyses of the multi-symplectic variational integrator for the nonlinear Schr o ¨ dinger equation are discussed in this paper. The variational integrator is proved to be unconditionally linearly stable using the von Neumann method. A priori error bound for the scheme is given from the Sobolev inequality and the discrete conservation laws. Subsequently, the variational integrator is derived to converge at O ( Δ x 2 + Δ t 2 ) in the discrete L 2 norm using the energy method. The numerical experimental results match our theoretical derivation.

Keywords: multi-symplectic variational integrator; stability; convergence; conservation laws; nonlinear Schrödinger equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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