riccati

riccati is a Python package implementing the adaptive Riccati defect correction (ARDC) method by Agocs & Barnett.

ARDC is a numerical method for solving ordinary diffential equations (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 subject to the initial conditions \(u(t_0) = u_0\), \(u'(t_0) = u'_0\).

This documentation will show you how to use the package which is under active development on GitHub.

Shields

How to use the docs

Start by following the (brief) Installation guide. After that you may get started straight away with the Quick Start, or check out some more Examples. Each function in the module is documented in the API.

User Guide

• Installation
  • Via package managers
  • Testing the installation
• Quick Start
• Examples
  • Quick summary of the algorithm
  • Basic example
  • \(\omega\), \(\gamma\) can be any callable
  • Optional and tuning parameters
  • Solving an ODE one step at a time
  • Benchmarks

Reference

• API

To generate offline documentation, get the source code as described in the Installation guide, and run

cd docs/
make html

This will create a docs/build/ directory in which the html/ subdirectory contains these documentation pages in html format.

License and attribution

Copyright 2022-2023 The Simons Foundation, Inc.

riccati is free software available under the Apache License 2.0, for details see the LICENSE.

If you use riccati in your work, please cite our paper (arxiv, BibTex).

Contributing

We welcome bug reports, patches, feature requests, and other comments via GitHub issues.