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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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File | Description | Size | Format | |
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paper 1.pdf | Peer-reviewed author version | 340.65 kB | Adobe PDF | View/Open |
1-s2.0-S0168927420302804-main.pdf Restricted Access | Published version | 692.36 kB | Adobe PDF | View/Open Request a copy |
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