(untitled) (Journal of Computational Mathematics, 2023)
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.