Stability of implicit multiderivative deferred correction methods

Abstract

Very recently, a novel class of parallelizable high-order time discretization schemes has been introduced in Schutz et al. (J Sci Comput 90(54):1-33, 2022). In this current work, we analyze the stability properties of those schemes and introduce a small but effective modification which only necessitates minor modifications of existing implementations. It is shown how this modification leads to A(a)-stable schemes with a being close to 90 degrees. Numerical examples illustrate an additional favorable influence of this modification on the accuracy of those schemes.