Leapfrog-Chebyshev and leapfrog-type multirate methods

The following codes contain implementations of leapfrog-Chebyshev (LFC) and leapfrog-type multirate methods for semilinear second order differential wave equations, developed and analyzed within the project A4.

For information about and possible applications of these schemes have a look at

• the paper On leapfrog-Chebyshev schemes by Constantin Carle, Marlis Hochbruck, and Andreas Sturm.
• the paper Error analysis of multirate leapfrog-type methods for second-order semilinear ODEs by Constantin Carle and Marlis Hochbruck.

Further information and some variants of these schemes are considered in the doctoral thesis On leapfrog-Chebyshev schemes for second-order diffferential equations by Constantin Carle.

Access to software

The codes are written in Python3. Further details about the requirements can be found in the corresponding Readme files which also contains a short summary about the included files.

The codes for the leapfrog-Chebyshev methods proposed in On leapfrog-Chebyshev schemes can be downloaded here (zip, ~540kb).

The codes for the leapfrog-type multirate methods used in the paper Error analysis of multirate leapfrog-type methods for second-order semilinear ODEs can be accessed here https://doi.org/10.5445/IR/1000133907.

The codes used in the thesis On leapfrog-Chebyshev schemes for second-order diffferential equations can be accessed here https://doi.org/10.5445/IR/1000147744.

We gratefully acknowledge financial support by the Deutsche Forschungsgemeinschaft (DFG) through CRC 1173.