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A three-level finite difference method with preconditioning technique for two-dimensional nonlinear fractional complex Ginzburg–Landau equations
Zhang,Qifeng1; Zhang,Lu2; Sun,Hai wei3
2021-06-01
Source PublicationJournal of Computational and Applied Mathematics
ISSN0377-0427
Volume389
AbstractIn the paper, we study two-dimensional nonlinear spatial fractional complex Ginzburg–Landau equations. A centered finite difference method is exploited to discretize the spatial variables, while a three-level finite difference scheme is applied for the time integration. Theoretically, we prove the proposed method is uniquely solvable and unconditionally stable, with second order accuracy on both time and space, respectively. As the resulting discretized systems possess the block-Toeplitz structure, we proposed the preconditioned GMRES method with a block circulant preconditioner to speed up the convergence rate of the iteration. Meanwhile, fast Fourier transformation is utilized to reduce the complexity for calculating the discretized systems. Numerical experiments are carried out to verify the theoretical results and demonstrate that the proposed method enjoys the excellent computational advantage.
KeywordBoundedness Circulant preconditioner Crank–Nicolson scheme Space fractional Ginzburg–Landau equation
DOI10.1016/j.cam.2020.113355
URLView the original
Language英语
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Cited Times [WOS]:2   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionUniversity of Macau
Affiliation1.Department of Mathematics,Zhejiang Sci-Tech University,Hangzhou,310018,China
2.School of Mathematics and Statistics,Xuzhou University of Technology,Xuzhou,Jiangsu,221018,China
3.Department of Mathematics,University of Macau,Macao,China
Recommended Citation
GB/T 7714
Zhang,Qifeng,Zhang,Lu,Sun,Hai wei. A three-level finite difference method with preconditioning technique for two-dimensional nonlinear fractional complex Ginzburg–Landau equations[J]. Journal of Computational and Applied Mathematics,2021,389.
APA Zhang,Qifeng,Zhang,Lu,&Sun,Hai wei.(2021).A three-level finite difference method with preconditioning technique for two-dimensional nonlinear fractional complex Ginzburg–Landau equations.Journal of Computational and Applied Mathematics,389.
MLA Zhang,Qifeng,et al."A three-level finite difference method with preconditioning technique for two-dimensional nonlinear fractional complex Ginzburg–Landau equations".Journal of Computational and Applied Mathematics 389(2021).
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