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

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.

Automated summary

This paper introduces a family of linear multistep second derivative methods based on barycentric rational interpolants, and investigates their order of convergence and linear stability. Numerical experiments are provided to validate the theoretical results and efficiency of the methods.