New stabilized explicit methods: Runge-Kutta-Legendre and Runge-Kutta-Gegenbauer methods

[ranocha]

What kind of problems is it mostly used for? Please describe.

Parabolic PDE discretization

Describe the algorithm you’d like

Implementations of the first- and second-order Runge-Kutta-Legendre and Runge-Kutta-Gegenbauer methods similar to ROCK2 to allow comparisons and more choices

Other implementations to know about

NA

References

• http://dx.doi.org/10.1016/j.jcp.2013.08.021
• https://doi.org/10.1111/j.1365-2966.2012.20744.x
• https://doi.org/10.1016/j.jcp.2020.109879
• https://arxiv.org/abs/2507.17062