SEMI-IMPLICIT SPECTRAL DEFERRED CORRECTION METHODS BASED ON SECOND-ORDER TIME INTEGRATION SCHEMES FOR NONLINEAR PDES  

作　　者：Ruihan Guo Yan Xu 

机构地区：[1]School of Mathematics and Statistics,Zhengzhou University,Zhengzhou 450001,China [2]School of Mathematical Sciences,University of Science and Technology of China,Hefei 230026,China

出　　处：《Journal of Computational Mathematics》2024年第1期111-133,共23页计算数学（英文）

基　　金：supported by NSFC(Grant No.11601490).Research of Y.Xu is supported by NSFC(Grant No.12071455).

摘　　要：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.

关 键 词：Spectral deferred correction method Nonlinear PDEs Local discontinuous Galerkin method Second-order scheme 

分 类 号：O17[理学—数学]