Year: 2023
Author: Boling Guo, Tingchun Wang, Shasha Bian, Yue Cheng, Boling Guo, Tingchun Wang
Numerical Mathematics: Theory, Methods and Applications, Vol. 16 (2023), Iss. 1 : pp. 140–164
Abstract
In this paper, we derive and analyze a conservative Crank-Nicolson-type finite difference scheme for the Klein-Gordon-Dirac (KGD) system. Differing from the derivation of the existing numerical methods given in literature where the numerical schemes are proposed by directly discretizing the KGD system, we translate the KGD equations into an equivalent system by introducing an auxiliary function, then derive a nonlinear Crank-Nicolson-type finite difference scheme for solving the equivalent system. The scheme perfectly inherits the mass and energy conservative properties possessed by the KGD, while the energy preserved by the existing conservative numerical schemes expressed by two-level's solution at each time step. By using energy method together with the 'cut-off' function technique, we establish the optimal error estimate of the numerical solution, and the convergence rate is $\mathcal{O}(τ^2 + h^2)$ in $l^∞$-norm with time step $τ$ and mesh size $h.$ Numerical experiments are carried out to support our theoretical conclusions.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2022-0049
Numerical Mathematics: Theory, Methods and Applications, Vol. 16 (2023), Iss. 1 : pp. 140–164
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Klein-Gordon-Dirac equation nonlinear finite difference scheme conservation error analysis.
Author Details
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Improved error estimates of the time‐splitting methods for the long‐time dynamics of the Klein–Gordon–Dirac system with the small coupling constant
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https://doi.org/10.1002/num.23084 [Citations: 1]