Non-iterative localized exponential time differencing method for hyperbolic conservation laws

Abstract: In this work, we introduce novel numerical methods for solving hyperbolic conservation laws. Since many existing schemes require some CFL conditions for stability, we employ the ETD-RK methods to eliminate these strict requirements. The problem is first discretized in space using the DG method before applying the ETD-RK scheme in time. To reduce the complexity of matrix exponential vector products, we further utilize the non-overlapping DD method with suitable transmission conditions to avoid iteratively solving nonlinear equations at each time step. Several numerical experiments are presented to verify the theoretical results and emphasize the performance of our proposed schemes in terms of CFL-free and shock-capturing properties. This marks the first proposal of the non-iterative localized ETD-RK method for hyperbolic conservation laws.

Last modified: Wed Mar 27 13:20:12 EDT 2024