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 diffusion-reaction type for which the reaction Jacobian has real (negative) eigenvalues. It is based on a family of implicit-explicit Runge-Kutta-Chebyshev 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: Runge-Kutta-Chebyshev methods; stiff reactions; stability; PDEs; time integration; diffusion-reaction equation; step size control; numerical examples; semidiscretization Related Software: RKC; RODAS; VODE; LSODA; MEBDF; SERK2v3; SERK2; DASSL; NSDTST; STDTST; GitHub; UMFPACK; ADOL-C; 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 diffusion-reaction PDEs. Zbl 1100.65075Shampine, L. F.; Sommeijer, B. P.; Verwer, J. G. 2006 all top 5 Cited by 39 Authors 5 González-Pinto, Severiano 4 Pérez Rodríguez, S. 3 Sommeijer, Ben P. 2 Hernandez-Abreu, Domingo 2 Laurent, Frédérique 2 Massot, Marc 2 Verwer, Jan G. 2 Xiao, Aiguo 1 Asante-Asamani, E. O. 1 Bozzini, Benedetto 1 Braś, Michał 1 Descombes, Stéphane 1 Duarte, Max 1 Dumont, Thierry 1 Dupays, Joël 1 Izzo, Giuseppe 1 Jackiewicz, Zdzislaw 1 Kleefeld, Andreas 1 Kühn, Christian 1 Lacitignola, Deborah 1 Lipoth, Jessica 1 Louvet, Violaine 1 Martín-Vaquero, Jesús 1 Murrone, Angelo 1 O’Sullivan, Stephen 1 Preuss, Adam 1 Ruprecht, Daniel 1 Seaïd, Mohammed 1 Sgura, Ivonne 1 Shampine, Lawrence Fred 1 Sibra, Alaric 1 Speck, Robert 1 Spiteri, Raymond J. 1 Tang, Xiao 1 Tenaud, Christian 1 Wade, Bruce A. 1 Yi, Xing 1 Zbinden, Christophe J. 1 Zhang, Gengen all top 5 Cited in 10 Serials 5 Journal of Computational and Applied Mathematics 4 Journal of Computational Physics 3 Applied Numerical Mathematics 2 SIAM Journal on Scientific Computing 1 Computer Physics Communications 1 Applied Mathematics and Computation 1 Mathematics and Computers in Simulation 1 Journal of Scientific Computing 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 1 Applied Mathematical Sciences all top 5 Cited in 9 Fields 19 Numerical analysis (65-XX) 11 Partial differential equations (35-XX) 4 Ordinary differential equations (34-XX) 2 Fluid mechanics (76-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Integral equations (45-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Biology and other natural sciences (92-XX) Citations by Year