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Numerical Algorithms
Published in: Numerical Algorithms 4/2020

02-03-2020 | Original Paper

Two energy-conserving and compact finite difference schemes for two-dimensional Schrödinger-Boussinesq equations

Authors: Feng Liao, Luming Zhang, Tingchun Wang

Published in: Numerical Algorithms | Issue 4/2020

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Abstract

In this paper, we study two compact finite difference schemes for the Schrödinger-Boussinesq (SBq) equations in two dimensions. The proposed schemes are proved to preserve the total mass and energy in the discrete sense. In our numerical analysis, besides the standard energy method, a “cut-off” function technique and a “lifting” technique are introduced to establish the optimal H1 error estimates without any restriction on the grid ratios. The convergence rate is proved to be of O(τ2 + h4) with the time step τ and mesh size h. In addition, a fast finite difference solver is designed to speed up the numerical computation of the proposed schemes. The numerical results are reported to verify the error estimates and conservation laws.
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Metadata
Title
Two energy-conserving and compact finite difference schemes for two-dimensional Schrödinger-Boussinesq equations
Authors
Feng Liao
Luming Zhang
Tingchun Wang
Publication date
02-03-2020
Publisher
Springer US
Published in
Numerical Algorithms / Issue 4/2020
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265
DOI
https://doi.org/10.1007/s11075-019-00867-8

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