High order methods are often desired for the evolution of ordinary differential equations, in particular those arising from the semi-discretization of partial differential equations. In prior work in we investigated the interplay between the local truncation error and the global error to construct error inhibiting general linear methods (GLMs) that control the accumulation of the local truncation error over time. Furthermore we defined sufficient conditions that allow us to post-process the final solution and obtain a solution that is two orders of accuracy higher than expected from truncation error analysis alone. In this work we extend this theory to two recently popular classes of methods: two-derivative GLMs and Implicit-Explicit GLMs. Both classes of methods can obtain high stage orders of accuracy, proving their effectiveness for solving stiff problems.
Dr. Grant received his PhD in Computational Science and Engineering from the University of Massachusetts Dartmouth in May 2018. His research interests primarily lie numerical analysis, high order methods for numerical PDEs, and developing novel temporal discretizations. In particular, his work focuses on designing new types of strong stability preserving time stepping schemes for the solution of hyperbolic conservation laws. He is currently a Alton S. Householder fellow in the Computational and Applied Mathematics group at the Oak Ridge National Laboratory.
Last Updated: May 28, 2020 - 4:01 pm