Eliminating Order Reduction on Linear, Time-Dependent ODEs with GARK Methods
| dc.contributor.author | Roberts, Steven | en |
| dc.contributor.author | Sandu, Adrian | en |
| dc.date.accessioned | 2022-02-27T04:00:48Z | en |
| dc.date.available | 2022-02-27T04:00:48Z | en |
| dc.date.issued | 2022-01-19 | en |
| dc.date.updated | 2022-02-27T04:00:48Z | en |
| dc.description.abstract | When applied to stiff, linear differential equations with time-dependent forcing, Runge-Kutta methods can exhibit convergence rates lower than predicted by the classical order condition theory. Commonly, this order reduction phenomenon is addressed by using an expensive, fully implicit Runge-Kutta method with high stage order or a specialized scheme satisfying additional order conditions. This work develops a flexible approach of augmenting an arbitrary Runge-Kutta method with a fully implicit method used to treat the forcing such as to maintain the classical order of the base scheme. Our methods and analyses are based on the general-structure additive Runge-Kutta framework. Numerical experiments using diagonally implicit, fully implicit, and even explicit Runge-Kutta methods confirm that the new approach elimi- nates order reduction for the class of problems under consideration, and the base methods achieve their theoretical orders of convergence. | en |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.orcid | Sandu, Adrian [0000-0002-5380-0103] | en |
| dc.identifier.uri | http://hdl.handle.net/10919/108889 | en |
| dc.language.iso | en | en |
| dc.relation.uri | http://arxiv.org/abs/2201.07940v2 | en |
| dc.rights | In Copyright | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject | math.NA | en |
| dc.subject | cs.NA | en |
| dc.subject | 65L04, 65L20 | en |
| dc.title | Eliminating Order Reduction on Linear, Time-Dependent ODEs with GARK Methods | en |
| dc.type | Article - Refereed | en |
| dc.type.dcmitype | Text | en |
| pubs.organisational-group | /Virginia Tech | en |
| pubs.organisational-group | /Virginia Tech/Engineering | en |
| pubs.organisational-group | /Virginia Tech/Engineering/Computer Science | en |
| pubs.organisational-group | /Virginia Tech/All T&R Faculty | en |
| pubs.organisational-group | /Virginia Tech/Engineering/COE T&R Faculty | en |
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