首页|A conservative scheme for two-dimensional Schrodinger equation based on multiquadric trigonometric quasi-interpolation approach

A conservative scheme for two-dimensional Schrodinger equation based on multiquadric trigonometric quasi-interpolation approach

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  • NSTL
  • Elsevier
In this paper, we propose a conservative scheme to solve the time-dependent twodimensional nonlinear Schrodinger equation, which plays an important role in many fields of physics. We discretize the equation using the multiquadric trigonometric quasi interpolation method in space and the Crank-Nicolson scheme in time. The quasiinterpolant is constructed through a linear combination of function values and node translations of a kernel function. It is very simple to compute since it doesn't need to solve any linear system. We adopt two different approaches to approximate second order spatial derivatives and analyze the symmetric or anti-symmetric properties of differentiation matrices. Moreover, the convergence and conservation properties including the total mass and energy conservation laws are also investigated in detail. Numerical experiments are performed to illustrate the accuracy and efficiency of the proposed method.(c) 2022 Elsevier Inc. All rights reserved.

Quasi-interpolationSchrodinger equationMultiquadric functionConservative schemesRELATIVE EQUILIBRIUM SOLUTIONSSPLINE FINITE-ELEMENTNUMERICAL-SOLUTIONPSEUDOSPECTRAL-METHODDIFFERENCE-SCHEMESGALERKIN METHODSINTEGRATIONDYNAMICSAPPROXIMATIONACCURACY

Sun, Zhengjie

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Nanjing Univ Sci & Technol

2022

10.1016/j.amc.2022.126996

Applied mathematics and computation

Applied mathematics and computation

EISCI
ISSN：0096-3003
年,卷(期)：2022.423
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