Numerical solution methods for implicit Runge-Kutta methods of arbitrarily high order

0559355 - ÚGN 2023 RIV SK eng C - Conference Paper (international conference)
Axelsson, Owe - Neytcheva, M.
Numerical solution methods for implicit Runge-Kutta methods of arbitrarily high order.
Proceedings of The Conference Algoritmy 2020. Bratislava: Slovak University of Technology in Bratislava, 2020 - (Frolkovič, P.; Mikula, K.; Ševčovič, D.), s. 11-20. ISBN 978-80-227-5032-5.
[Algoritmy 2020 - Conference on Scientific Computing /21./. Vysoké Tatry - Podbanské (SK), 10.09.2020-15.09.2020]
R&D Projects: GA MŠMT LQ1602
Institutional support: RVO:68145535
Keywords : implicit Runge-Kutta methods * Radau methods * iterative methods * preconditioning * fully stage-parallel
OECD category: Applied mathematics
http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/download/1546/810

In this study we consider an efficient implementation of Implicit Runge-Kutta methods for solving large systems of ordinary differential equations that originate from finite element discretization of the heat and similar equations, to be solved on large time intervals. The main contribution of this work is to show how to implement a fully stage-parallel version of the method, utilizing the dominance of the block lower triangular part of the quadrature matrix, and to illustrate it numerically. Its usage for the solution of algebraic-differential equations is also touched.
Permanent Link: https://hdl.handle.net/11104/0332701