Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/32401
Title: An asymptotic preserving semi-implicit multiderivative solver
Authors: SCHUETZ, Jochen 
Seal, David
Issue Date: 2021
Publisher: 
Source: Applied numerical mathematics, 160 , p. 84 -101
Abstract: In this work we construct a multiderivative implicit-explicit (IMEX) scheme for a class of stiff ordinary differential equations (ODEs). Our solver is high-order accurate and has an asymptotic preserving (AP) property for a large class of singularly perturbed ODEs. In this context, the AP property means that the singular limit is discretely preserved when a stiff parameter εgoes to zero. The proposed method is based upon a two-derivative backward Taylor series base solver, which we show has an AP property. Higher order accuracies are found by iterating the result over a high-order multiderivative interpolant of the right hand side function, which we again prove has an AP property. Theoretical results showcasing the asymptotic consistency as well as the high-order accuracy of the solver are presented. In addition, an extension of the solver to an arbitrarily split right hand side function is also offered. Numerical results for a collection of standard test cases from the literature are presented that support the theoretical findings of the paper.
Keywords: Multiderivative;IMEX;Singularly perturbed ODE;Asymptotic preserving
Document URI: http://hdl.handle.net/1942/32401
ISSN: 0168-9274
e-ISSN: 1873-5460
DOI: 10.1016/j.apnum.2020.09.004
ISI #: WOS:000587835300005
Rights: Published by Elsevier B.V. on behalf of IMACS.
Category: A1
Type: Journal Contribution
Validations: ecoom 2021
Appears in Collections:Research publications

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