A numerical investigation of nonlinear Schrödinger equation using barycentric interpolation collocation method

Haoran Sun; Siyu Huang; Mingyang Zhou; Yilun Li; Zhifeng Weng; Haoran Sun; Siyu Huang; Mingyang Zhou; Yilun Li; Zhifeng Weng

doi:10.3934/math.2023017

AIMS Mathematics

2023, Volume 8, Issue 1: 361-381. doi: 10.3934/math.2023017

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Research article

A numerical investigation of nonlinear Schrödinger equation using barycentric interpolation collocation method

Fujian Province University Key Laboratory of Computation Science, School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China

Received: 03 May 2022 Revised: 19 August 2022 Accepted: 05 September 2022 Published: 30 September 2022
MSC : 65M70, 65L20

In this paper, we will present a collocation approach based on barycentric interpolation functions and finite difference formulation to study the approximate solution of nonlinear Schrödinger equation. We discretize the time derivative by Crank-Nicolson scheme and bring barycentric interpolation functions into action for spatial discretization. Furthermore, consistency analysis of semi discrete collocation scheme is given. For the nonlinear term, we use Newton iterative method to derive the corresponding linear algebraic equations. Finally, numerical examples show that the numerical scheme has high precision and satisfies the mass and energy conservation.
- barycentric interpolation collocation,
- nonlinear Schrödinger equation,
- consistency analysis,
- mass and energy conservation
Citation: Haoran Sun, Siyu Huang, Mingyang Zhou, Yilun Li, Zhifeng Weng. A numerical investigation of nonlinear Schrödinger equation using barycentric interpolation collocation method[J]. AIMS Mathematics, 2023, 8(1): 361-381. doi: 10.3934/math.2023017

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Abstract

In this paper, we will present a collocation approach based on barycentric interpolation functions and finite difference formulation to study the approximate solution of nonlinear Schrödinger equation. We discretize the time derivative by Crank-Nicolson scheme and bring barycentric interpolation functions into action for spatial discretization. Furthermore, consistency analysis of semi discrete collocation scheme is given. For the nonlinear term, we use Newton iterative method to derive the corresponding linear algebraic equations. Finally, numerical examples show that the numerical scheme has high precision and satisfies the mass and energy conservation.

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