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A software platform...
A software platform for adaptive high order multistep methods
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- Arévalo, Carmen (author)
- Lund University,Lunds universitet,Numerisk analys,Forskargrupper vid Lunds universitet,Numerical Analysis,Lund University Research Groups
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- Jonsson-Glans, Erik (author)
- HiQ Ace AB
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- Olander, Josefine (author)
- HiQ Ace AB
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- Soto, Monica Selva (author)
- University of Concepción
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- Söderlind, Gustaf (author)
- Lund University,Lunds universitet,Numerisk analys,Forskargrupper vid Lunds universitet,Numerical Analysis,Lund University Research Groups
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(creator_code:org_t)
- 2020-03-20
- 2020
- English.
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In: ACM Transactions on Mathematical Software. - : Association for Computing Machinery (ACM). - 0098-3500 .- 1557-7295. ; 46:1
- Related links:
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http://dx.doi.org/10...
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Abstract
Subject headings
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- We present a software package, Modes, offering h-adaptive and p-adaptive linear multistep methods for first order initial value problems in ordinary differential equations. The implementation is based on a new parametric, grid-independent representation of multistep methods [Arévalo and Söderlind 2017]. Parameters are supplied for over 60 methods. For nonstiff problems, all maximal order methods (p=k for explicit and p=k+1 for implicit methods) are supported. For stiff computation, implicit methods of order p=k are included. A collection of step-size controllers based on digital filters is provided, generating smooth step-size sequences offering improved computational stability. Controllers may be selected to match method and problem classes. A new system for automatic order control is also provided for designated families of multistep methods, offering simultaneous h- and p-adaptivity. Implemented as a Matlab toolbox, the software covers high order computations with linear multistep methods within a unified, generic framework. Computational experiments show that the new software is competitive and offers qualitative improvements. Modes is available for downloading and is primarily intended as a platform for developing a new generation of state-of-the-art multistep solvers, as well as for true ceteris paribus evaluation of algorithmic components. This also enables method comparisons within a single implementation environment.
Subject headings
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
- TEKNIK OCH TEKNOLOGIER -- Elektroteknik och elektronik -- Reglerteknik (hsv//swe)
- ENGINEERING AND TECHNOLOGY -- Electrical Engineering, Electronic Engineering, Information Engineering -- Control Engineering (hsv//eng)
Keyword
- multistep methods
- ordinary differential equations
- Solver
- variable order
- variable step size
Publication and Content Type
- art (subject category)
- ref (subject category)
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