TY - JOUR
T1 - Semi-Implicit Spectral Deferred Correction Methods Based on Second-Order Time Integration Schemes for Nonlinear PDEs
AU - Guo , Ruihan
AU - Xu , Yan
JO - Journal of Computational Mathematics
VL - 1
SP - 111
EP - 133
PY - 2023
DA - 2023/12
SN - 42
DO - http://doi.org/10.4208/jcm.2202-m2021-0302
UR - https://global-sci.org/intro/article_detail/jcm/22154.html
KW - Spectral deferred correction method, Nonlinear PDEs, Local discontinuous
Galerkin method, Second-order scheme.
AB - <p style="text-align: justify;">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.</p>