The {sc fortran program {sc rkc is intended for the time integration of parabolic partial differential equations discretized by the method of lines. It is based on a family of Runge-Kutta-Chebyshev formulas with a stability bound that is quadratic in the number of stages. Remarkable properties of the family make it possible for the program to select at each step the most efficient stable formula as well as the most efficient step size. Moreover, they make it possible to evaluate the explicit formulas in just a few vectors of storage. These characteristics of the program make it especially attractive for problems in several spatial variables. {sc rkc is compared to the {sc bdf solver {sc vodpk on two test problems in three spatial variables.

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Modelling, Analysis and Simulation [MAS]
Computational Dynamics

Sommeijer, B., Shampine, L. F., & Verwer, J. (1997). RKC : an explicit solver for parabolic PDEs. Modelling, Analysis and Simulation [MAS]. CWI.