Design of DIRK schemes with high weak stage order

Abhijit Biswas, David I. Ketcheson, Benjamin Seibold, David Shirokoff

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Runge–Kutta (RK) methods may exhibit order reduction when applied to certain stiff problems. While fully implicit RK schemes exist that avoid order reduction via high-stage order, DIRK (diagonally implicit Runge–Kutta) schemes are practically important due to their structural simplicity; however, these cannot possess high stage order. The concept of weak stage order (WSO) can also overcome order reduction, and it is compatible with the DIRK structure. DIRK schemes of WSO up to 3 have been proposed in the past, however, they were based on a simplified framework that cannot be extended beyond WSO 3. In this work a general theory of WSO is employed to overcome the prior WSO barrier and to construct practically useful high-order DIRK schemes with WSO 4 and above. The resulting DIRK schemes are stiffly accurate, L-stable, have optimized error coefficients, and are demonstrated to perform well on a portfolio of relevant ODE and PDE test problems.
Original languageEnglish (US)
Pages (from-to)1-28
Number of pages28
JournalCommunications in Applied Mathematics and Computational Science
Issue number1
StatePublished - May 24 2023

ASJC Scopus subject areas

  • Computer Science Applications
  • Applied Mathematics
  • Computational Theory and Mathematics


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