DIRK Schemes with High Weak Stage Order

Benjamin Seibold; David Ketcheson; David Shirokoff; Dong Zhou

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arxiv 1811.01285 v2 pith:IDVWJTCJ submitted 2018-11-03 math.NA cs.NA

DIRK Schemes with High Weak Stage Order

David Ketcheson , Benjamin Seibold , David Shirokoff , Dong Zhou This is my paper

classification math.NA cs.NA

keywords orderstagedirkreductionschemesweakhighmethods

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Runge-Kutta time-stepping methods in general suffer from order reduction: the observed order of convergence may be less than the formal order when applied to certain stiff problems. Order reduction can be avoided by using methods with high stage order. However, diagonally-implicit Runge-Kutta (DIRK) schemes are limited to low stage order. In this paper we explore a weak stage order criterion, which for initial boundary value problems also serves to avoid order reduction, and which is compatible with a DIRK structure. We provide specific DIRK schemes of weak stage order up to 3, and demonstrate their performance in various examples.

DIRK Schemes with High Weak Stage Order

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