Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

The Convergence of Discrete Models for Nonlinear Schrödinger Equation in Dark Solitons Motion

Version 1 : Received: 22 May 2023 / Approved: 23 May 2023 / Online: 23 May 2023 (07:45:25 CEST)

A peer-reviewed article of this Preprint also exists.

Li, Y.; Luo, Q.; Feng, Q. The Convergence of Symmetric Discretization Models for Nonlinear Schrödinger Equation in Dark Solitons’ Motion. Symmetry 2023, 15, 1229. Li, Y.; Luo, Q.; Feng, Q. The Convergence of Symmetric Discretization Models for Nonlinear Schrödinger Equation in Dark Solitons’ Motion. Symmetry 2023, 15, 1229.

Abstract

We firstly present two popular space discretization models of the Nonlinear Schrödinger Equation in dark solitons motion : the Direct-Discrete model and the Ablowitz-Ladik model. Applying the midpoint scheme to the space discretization models, we get two time-space discretization models: the Crank-Nicolson method and the New-Difference method. Secondly, we demonstrate that the solutions of the two space discretization models converge to the solution of the Nonlinear Schrödinger Equation. Also, we prove that the convergence order of the two time-space discretization models are O(h2+τ2) in discrete L2-norm error estimates. Finally, the numerical experiments agree well with the proven theoretical results.

Keywords

Nonlinear schrödinger equation; Space discretization models; Time-space discretization models; Crank-Nicolson method; New-Difference method.

Subject

Computer Science and Mathematics, Mathematics

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