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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/23916

Title: Implicit Multiderivative Collocation Solvers for Linear Partial Differential Equations with Discontinuous Galerkin Spatial Discretizations
Authors: Schütz, Jochen
Seal, David C.
Jaust, Alexander
Issue Date: 2017
Citation: JOURNAL OF SCIENTIFIC COMPUTING, 73 (2-3), p. 1145-1163
Status: In Press
Abstract: In this work, we construct novel discretizations for the unsteady convection–diffusion equation. Our discretization relies on multiderivative time integrators together with a novel discretization that reduces the total number of unkowns for the solver. These type of temporal discretizations come from an umbrella class of methods that include Lax–Wendroff (Taylor) as well as Runge–Kutta methods as special cases. We include two-point collocation methods with multiple time derivatives as well as a sixth-order fully implicit collocation method that only requires a total of three stages. Numerical results for a number of sample linear problems indicate the expected order of accuracy and indicate we can take arbitrarily large time steps.
Notes: Schutz, J (reprint author), Hasselt Univ, Computat Math Grp, Fac Sci, Agoralaan Gebouw D, B-3590 Diepenbeek, Belgium. jochen.schuetz@uhasselt.be; seal@usna.edu; alexander.jaust@uhasselt.be
URI: http://hdl.handle.net/1942/23916
DOI: 10.1007/s10915-017-0485-9
ISI #: 000414478700028
ISSN: 0885-7474
Category: A1
Type: Journal Contribution
Validation: ecoom, 2018
Appears in Collections: Research publications

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