High-order multiderivative IMEX schemes

Recently, a 4th-order asymptotic preserving multiderivative implicit-explicit (IMEX) scheme was developed [28] . This is based on Hermite interpolation in time, and uses an approach operator splitting that converges to the underlying quadrature if iterated sufficiently. schemes have been used astrophysics for decades, particularly N-body calculations, but not form suitable solving stiff equations. In this work, we extend higher orders. Such high-order offer advantages when one aims find high-precision solutions systems of differential equations containing terms, which occur throughout physical sciences. We begin by deriving Hermit arbitrary order demonstrating how IMEX method generalises straightforward manner any these schemes. Afterwards, discuss stability schemes, prove convergence properties corresponding methods. then present results methods ranging from 6th 12th explore selection test problems, including both linear nonlinear ordinary as well Burgers' equation. To our knowledge also first time time-stepping applied partial some benefits such their potential parallelism low memory usage, limitations drawbacks.