High-Order Stabilization in Semi-Implicit Deferred Correction Methods

Source abstract

In this paper, we construct high-order stabilization terms for semi-implicit deferred correction methods, focusing on convection-diffusion-reaction problems. Optimal choices for stability parameters are investigated and the upper bounds of the time step to ensure both stability and high-order accuracy are analyzed. Utilizing Fourier analysis, we apply von Neumann stability and Schur theory to new single- and multi-step deferred correction methods. Numerical experiments validate the analysis of the stability parameter estimates and time step constraints for these methods.