adaptive Riccati defect correction solver
Project description
riccati
A package implementing the adaptive Riccati defect correction (ARDC) method
About
riccati
is a Python
package for solving ODEs of the form
$$ u''(t) + 2\gamma(t)u'(t) + \omega^2(t)u(t) = 0,$$
on some solution interval $t \in [t_0, t_1]$, and with initial conditions $u(t_0) = u_0$, $u'(t_0) = u'_0$.
riccati
uses the adaptive Riccati defect correction method -- it switches
between using nonoscillatory (spectral Chebyshev) and a specialised oscillatory
solver (Riccati defect correction) to propagate the numerical solution based on
its behaviour. More details here: ...
Documentation
Read the documentation at riccati.readthedocs.io.
Attribution
If you find this code useful in your research, please cite Agocs & Barnett (2022). Its BibTeX entry is
@ARTICLE{ardc,
author = {{Agocs}, Fruzsina J. and {Barnett}, Alex H.},
title = "{An adaptive spectral method for oscillatory second-order
linear ODEs with frequency-independent cost}",
journal = {arXiv e-prints},
keywords = {Mathematics - Numerical Analysis},
year = 2022,
month = dec,
eid = {arXiv:2212.06924},
pages = {arXiv:2212.06924},
doi = {10.48550/arXiv.2212.06924},
archivePrefix = {arXiv},
eprint = {2212.06924},
primaryClass = {math.NA},
adsurl = {https://ui.adsabs.harvard.edu/abs/2022arXiv221206924A},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
License
Copyright 2022-2023 The Simons Foundation, Inc.
riccati is free software available under the Apache License 2.0, for details see the LICENSE.
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