Semi-Implicit Spectral Deferred Correction Methods Based on Second-Order Time Integration Schemes for Nonlinear PDEs
Year: 2024
Author: Ruihan Guo, Yan Xu
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 1 : pp. 111–133
Abstract
In [20], a semi-implicit spectral deferred correction (SDC) method was proposed, which is efficient for highly nonlinear partial differential equations (PDEs). The semi-implicit SDC method in [20] is based on first-order time integration methods, which are corrected iteratively, with the order of accuracy increased by one for each additional iteration. In this paper, we will develop a class of semi-implicit SDC methods, which are based on second-order time integration methods and the order of accuracy are increased by two for each additional iteration. For spatial discretization, we employ the local discontinuous Galerkin (LDG) method to arrive at fully-discrete schemes, which are high-order accurate in both space and time. Numerical experiments are presented to demonstrate the accuracy, efficiency and robustness of the proposed semi-implicit SDC methods for solving complex nonlinear PDEs.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2202-m2021-0302
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 1 : pp. 111–133
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Spectral deferred correction method Nonlinear PDEs Local discontinuous Galerkin method Second-order scheme.
Author Details
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Stability of implicit deferred correction methods based on BDF methods
Yao, Lin
Xia, Yinhua
Xu, Yan
Applied Mathematics Letters, Vol. 158 (2024), Iss. P.109255
https://doi.org/10.1016/j.aml.2024.109255 [Citations: 0]