 Convergence analysis of two conservative finite difference fourier pseudo-spectral schemes for klein-Gordon-Dirac systemXianfen Wang and Jiyong Li Applied Mathematics and Computation, 2023, vol. 439, issue C Abstract: In this paper, we propose and study two conservative finite difference Fourier pseudo-spectral schemes numerically solving the Klein-Gordon-Dirac (KGD) system with periodic boundary conditions. The resulting numerical schemes are time symmetric and proved to conserve the discrete mass and the discrete energy. We give a rigorously convergence analysis for the schemes. Specifically, we establish the error estimates which are without any restrictions (CFL condition) on the ratio of time step to space step. The convergence rates of the new schemes are proved to be the temporal second-order and spatial spectral-order, respectively, in a Hm-norm. The main proof tools include the ideas of standard mathematical induction and the method of defining energy. Finally, we give the numerical experiments to support our theoretical analysis and error bounds. Keywords: Fourier pseudo-spectral method; Error estimates; Klein-Gordon-Dirac system; Finite difference method; Convergence analysis (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:439:y:2023:i:c:s0096300322007068 DOI: 10.1016/j.amc.2022.127634 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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