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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Abdi, A., Hojjati, G. Second derivative backward differentiation formulae for ODEs based on barycentric rational interpolants. Numer Algor 87, 1577–1591 (2021). https://doi.org/10.1007/s11075-020-01020-6
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DOI: https://doi.org/10.1007/s11075-020-01020-6
Keywords
- Ordinary differential equations
- Stiff problems
- Barycentric rational interpolation
- Barycentric rational finite differences
- Second derivative methods
- Linear stability