Convergence Results for Implicit--Explicit General Linear Methods

Adrian Sandu

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arXiv · 2004.04274

Convergence Results for Implicit--Explicit General Linear Methods

Adrian Sandu

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Abstract

This paper studies fixed-step convergence of implicit-explicit general linear methods. We focus on a subclass of schemes that is internally consistent, has high stage order, and favorable stability properties. Classical, index-1 differential algebraic equation, and singular perturbation convergence analyses results are given. For all these problems IMEX GLMs from the class of interest converge with the full theoretical orders under general assumptions. The convergence results require the time steps to be sufficiently small, with upper bounds that are independent on the stiffness of the problem.

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Adrian Sandu. 2020-04-08. Convergence Results for Implicit--Explicit General Linear Methods. https://arxiv.org/abs/2004.04274

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