On the stability of Approximate Taylor methods for ODE and their relationship with Runge-Kutta schemes
Numerical Analysis
2018-04-11 v1
Abstract
In [Baeza et al., Computers and Fluids, 159, 156--166 (2017)] a new method for the numerical solution of ODEs is presented. This methods can be regarded as an approximate formulation of the Taylor methods and it follows an approach that has a much easier implementation than the original Taylor methods, since only the functions in the ODEs, and not their high order derivatives, are needed. In this reference, the absolute stability region of the new methods is conjectured to be coincident with that of their exact counterparts. There is also a conjecture about their relationship with Runge-Kutta methods. In this work we answer positively both conjectures.
Keywords
Cite
@article{arxiv.1804.03627,
title = {On the stability of Approximate Taylor methods for ODE and their relationship with Runge-Kutta schemes},
author = {Antonio Baeza and Sebastiano Boscarino and Pep Mulet and Giovanni Russo and David Zorío},
journal= {arXiv preprint arXiv:1804.03627},
year = {2018}
}