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Numerical Algorithms
Published in: Numerical Algorithms 4/2021

14-10-2020 | Original Paper

Second derivative backward differentiation formulae for ODEs based on barycentric rational interpolants

Authors: Ali Abdi, Gholamreza Hojjati

Published in: Numerical Algorithms | Issue 4/2021

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Abstract

For their several attractive features from the viewpoint of the numerical computations, linear barycentric rational interpolants have been recently used to construct various numerical methods for solving different classes of equations. In this paper, we introduce a family of linear multistep second derivative methods together with a starting procedure based on barycentric rational interpolants. The order of convergence and linear stability properties of the proposed methods have been investigated. To validate the theoretical results and efficiency of the methods, some numerical experiments have been provided.
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Metadata
Title
Second derivative backward differentiation formulae for ODEs based on barycentric rational interpolants
Authors
Ali Abdi
Gholamreza Hojjati
Publication date
14-10-2020
Publisher
Springer US
Published in
Numerical Algorithms / Issue 4/2021
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265
DOI
https://doi.org/10.1007/s11075-020-01020-6

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