A Software Platform for Adaptive High Order Multistep Methods

Autor: Monica Selva Soto, Gustaf Söderlind, Carmen Arévalo, Erik Jonsson-Glans, Josefine Olander
Rok vydání: 2020
Předmět:
Zdroj: ACM Transactions on Mathematical Software. 46:1-17
ISSN: 1557-7295
0098-3500
DOI: 10.1145/3372159
Popis: We present a software package, M odes , 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 M atlab 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. M odes 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.
Databáze: OpenAIRE
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