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

Zhengjie Sun

Applied Mathematics and Computation, 2022, vol. 423, issue C

Abstract: In this paper, we propose a conservative scheme to solve the time-dependent two-dimensional nonlinear Schrödinger 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 quasi-interpolant 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.

Keywords: Quasi-interpolation; Schrödinger equation; Multiquadric function; Conservative schemes (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:423:y:2022:i:c:s0096300322000820

DOI: 10.1016/j.amc.2022.126996

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