publication . Preprint . 2017

Spatial Manifestations of Order Reduction in Runge-Kutta Methods for Initial Boundary Value Problems

Rosales, Rodolfo Ruben; Seibold, Benjamin; Shirokoff, David; Zhou, Dong;
Open Access English
  • Published: 03 Dec 2017
Abstract
This paper studies the spatial manifestations of order reduction that occur when time-stepping initial-boundary-value problems (IBVPs) with high-order Runge-Kutta methods. For such IBVPs, geometric structures arise that do not have an analog in ODE IVPs: boundary layers appear, induced by a mismatch between the approximation error in the interior and at the boundaries. To understand those boundary layers, an analysis of the modes of the numerical scheme is conducted, which explains under which circumstances boundary layers persist over many time steps. Based on this, two remedies to order reduction are studied: first, a new condition on the Butcher tableau, call...
Subjects
arXiv: Mathematics::Numerical Analysis
free text keywords: Mathematics - Numerical Analysis, 65L20, 65M15, 34E05
Funded by
NSF| Collaborative Research: Overcoming Order Reduction and Stability Restrictions in High-Order Time-Stepping
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 1719693
  • Funding stream: Directorate for Mathematical & Physical Sciences | Division of Mathematical Sciences
,
NSF| Collaborative Research: Overcoming Order Reduction and Stability Restrictions in High-Order Time-Stepping
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 1719640
  • Funding stream: Directorate for Mathematical & Physical Sciences | Division of Mathematical Sciences
,
NSF| Collaborative Research: Overcoming Order Reduction and Stability Restrictions in High-Order Time-Stepping
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 1719637
  • Funding stream: Directorate for Mathematical & Physical Sciences | Division of Mathematical Sciences
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