IRKC
swMATH ID:  452 
Software Authors:  Shampine, L.F.; Sommeijer, B.P.; Verwer, J.G. 
Description:  The Fortran 90 code IRKC is intended for the time integration of systems of partial differential equations (PDEs) of diffusionreaction type for which the reaction Jacobian has real (negative) eigenvalues. It is based on a family of implicitexplicit RungeKuttaChebyshev methods which are unconditionally stable for reaction terms and which impose a stability constraint associated with the diffusion terms that is quadratic in the number of stages. Special properties of the family make it possible for the code to select at each step the most efficient stable method as well as the most efficient step size. Moreover, they make it possible to apply the methods using just a few vectors of storage. A further step towards minimal storage requirements and optimal efficiency is achieved by exploiting the fact that the implicit terms, originating from the stiff reactions, are not coupled over the spatial grid points. Hence, the systems to be solved have a small dimension (viz., equal to the number of PDEs). These characteristics of the code make it especially attractive for problems in several spatial variables. IRKC is a successor to the RKC code of {\it B. P. Sommeijer, L. F. Shampine}, and {\it J. G. Verwer}, RKC: an explicit solver for parabolic PDEs, J. Comput. Appl. Math. 88, No. 2, 315–326 (1997; Zbl 0910.65067)] that solves similar problems without stiff reaction terms. 
Homepage:  http://www.netlib.org/ode/irkc.f90 
Keywords:  RungeKuttaChebyshev methods; stiff reactions; stability; PDEs; time integration; diffusionreaction equation; step size control; numerical examples; semidiscretization 
Related Software:  RKC; RODAS; VODE; LSODA; MEBDF; SERK2v3; SERK2; DASSL; NSDTST; STDTST; GitHub; UMFPACK; ADOLC; M3RK; CEDRE; CVODE; PIROCK; pySDC; Matplotlib; SciPy 
Cited in:  21 Publications 
Standard Articles
1 Publication describing the Software, including 1 Publication in zbMATH  Year 

IRKC: an IMEX solver for stiff diffusionreaction PDEs. Zbl 1100.65075 Shampine, L. F.; Sommeijer, B. P.; Verwer, J. G. 
2006

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Cited by 39 Authors
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Cited in 10 Serials
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