IRKC: an IMEX solver for stiff diffusion-reaction PDEs

The Fortran 90 program IRKC is intended for the time integration of partial differential equations (PDEs) of diffusion-reaction type for which the reaction Jacobian has real (negative) eigenvalues. It is based on a family of implicit-explicit Runge-Kutta-Chebyshev formulas which are unconditionally stable for reaction terms and which provide a stability bound for the diffusion terms that is quadratic in the number of stages. Special 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 formulas in just a few vectors of storage. These characteristics of the program make it especially attractive for problems in several spatial variables. IRKC is a successor to the RKC code of [5] that solves similar problems without stiff reaction terms