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- Publisher
- Springer Journals
- Copyright
- Copyright © Pleiades Publishing, Ltd. 2021
- ISSN
- 0012-2661
- eISSN
- 1608-3083
- DOI
- 10.1134/s0012266121070089
- Publisher site
- See Article on Publisher Site
Abstract
We consider Runge–Kutta methods whose stability domain includes a disk of maximumdiameter for given number of stages and order. These methods are used to solve initial valueproblems obtained by approximating hyperbolic systems with the use of the discontinuousGalerkin method. Two three-stage methods in the class in question are proposed for which, usingtest problems for the transport equation and for the system of gasdynamic equations, we studythe possibility to maintain the stability and monotonicity of the numerical solution with themaximum possible time steps.
Journal
Differential Equations – Springer Journals
Published: Jul 1, 2021