A software platform for adaptive high order multistep methods
(2020) In ACM Transactions on Mathematical Software 46(1).- Abstract
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... (More)
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.
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- author
- Arévalo, Carmen LU ; Jonsson-Glans, Erik ; Olander, Josefine ; Soto, Monica Selva and Söderlind, Gustaf LU
- organization
- publishing date
- 2020-04
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- multistep methods, ordinary differential equations, Solver, variable order, variable step size
- in
- ACM Transactions on Mathematical Software
- volume
- 46
- issue
- 1
- article number
- 2
- publisher
- Association for Computing Machinery (ACM)
- external identifiers
-
- scopus:85084748673
- ISSN
- 0098-3500
- DOI
- 10.1145/3372159
- language
- English
- LU publication?
- yes
- id
- c2d60224-0d45-4d34-9011-936e0ed4b1f6
- date added to LUP
- 2020-06-10 11:04:06
- date last changed
- 2022-04-18 22:54:11
@article{c2d60224-0d45-4d34-9011-936e0ed4b1f6,
abstract = {{<p>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.</p>}},
author = {{Arévalo, Carmen and Jonsson-Glans, Erik and Olander, Josefine and Soto, Monica Selva and Söderlind, Gustaf}},
issn = {{0098-3500}},
keywords = {{multistep methods; ordinary differential equations; Solver; variable order; variable step size}},
language = {{eng}},
number = {{1}},
publisher = {{Association for Computing Machinery (ACM)}},
series = {{ACM Transactions on Mathematical Software}},
title = {{A software platform for adaptive high order multistep methods}},
url = {{http://dx.doi.org/10.1145/3372159}},
doi = {{10.1145/3372159}},
volume = {{46}},
year = {{2020}},
}