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. For more details on the algorithm, please see Attribution.

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.