Symplectic Runge-Kutta Methods for Degenerate Lagrangian Systems

This packages serves to document the examples from the paper Symplectic Runge-Kutta Methods for Degenerate Lagrangian Systems. The integrators are implemented in GeometricIntegrators.jl in the modules GeometricIntegrators.Integrators and GeometricIntegrators.Integrators.VPRK, and the example problems in GeometricProblems.jl.

Numerical Examples

Lotka-Volterra 2d (singular Lagrangian)

• Symplectic Gauss-Legendre Runge-Kutta Methods
• Gauss-Legendre Runge-Kutta Methods
• Gauss-Legendre VPRK Methods
• Lobatto IIIA-IIIB VPRK Methods
• Lobatto IIIB-IIIA VPRK Methods
• Radau IIA VPRK Methods

Lotka-Volterra 2d (symmetric Lagrangian)

• Symplectic Gauss-Legendre Runge-Kutta Methods
• Gauss-Legendre Runge-Kutta Methods
• Gauss-Legendre VPRK Methods
• Lobatto IIIA-IIIB VPRK Methods
• Lobatto IIIB-IIIA VPRK Methods
• Radau IIA VPRK Methods

References

• Michael Kraus. Symplectic Runge-Kutta Methods for Degenerate Lagrangian Systems.

If you use the integrators described in the article above, please cite GeometricIntegrators.jl as

@misc{Kraus:2020:GeometricIntegrators,
  title={GeometricIntegrators.jl: Geometric Numerical Integration in Julia},
  author={Kraus, Michael},
  year={2020},
  howpublished={\url{https://github.com/JuliaGNI/GeometricIntegrators.jl}},
  doi={10.5281/zenodo.3648325}
}

If you use the figures or implementations provided here, please cite this repository as

@misc{Kraus:2020:SRKMethodsRepo,
  title={Companion Repository to ``Symplectic {R}unge--{K}utta Methods for Degenerate {L}agrangian Systems''},
  author={Kraus, Michael},
  year={2020},
  month={11},
  howpublished={\url{https://github.com/michakraus/paper-srk-methods-for-degenerate-lagrangian-systems}},
  doi={10.5281/zenodo.4285894}
}

Figure License

Copyright (c) Michael Kraus <michael.kraus@ipp.mpg.de>

All figures are licensed under the Creative Commons CC BY-NC-SA 4.0 License.

Software License

Copyright (c) Michael Kraus <michael.kraus@ipp.mpg.de>

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.