Semi-Implicit Spectral Deferred Correction Methods Based on Second-Order Time Integration Schemes for Nonlinear PDEs (Journal of Computational Mathematics, 2023)
In [20], a semi-implicit spectral deferred correction (SDC) method was proposed, whichis efficient for highly nonlinear partial differential equations (PDEs). The semi-implicitSDC method in [20] is based on first-order time integration methods, which are correctediteratively, with the order of accuracy increased by one for each additional iteration. Inthis paper, we will develop a class of semi-implicit SDC methods, which are based onsecond-order time integration methods and the order of accuracy are increased by two foreach additional iteration. For spatial discretization, we employ the local discontinuousGalerkin (LDG) method to arrive at fully-discrete schemes, which are high-order accuratein both space and time. Numerical experiments are presented to demonstrate the accuracy,efficiency and robustness of the proposed semi-implicit SDC methods for solving complexnonlinear PDEs.