PIROCK swMATH ID: 10253 Software Authors: Abdulle, Assyr; Vilmart, Gilles Description: PIROCK: A swiss-knife partitioned implicit-explicit orthogonal Runge-Kutta Chebyshev integrator for stiff diffusion-advection-reaction problems with or without noise. A partitioned implicit-explicit orthogonal Runge-Kutta method (PIROCK) is proposed for the time integration of diffusion-advection-reaction problems with possibly severely stiff reaction terms and stiff stochastic terms. The diffusion terms are solved by the explicit second order orthogonal Chebyshev method (ROCK2), while the stiff reaction terms (solved implicitly) and the advection and noise terms (solved explicitly) are integrated in the algorithm as finishing procedures. It is shown that the various coupling (between diffusion, reaction, advection and noise) can be stabilized in the PIROCK method. The method, implemented in a single black-box code that is fully adaptive, provides error estimators for the various terms present in the problem, and requires from the user solely the right-hand side of the differential equation. Numerical experiments and comparisons with existing Chebyshev methods, IMEX methods and partitioned methods show the efficiency and flexibility of our new algorithm. Homepage: http://www.sciencedirect.com/science/article/pii/S0021999113001198 Keywords: stabilized second-order integration method; stiff problems; advection-diffusion-reaction problems; stochastic problems; partitioned implicit-explicit orthogonal Runge-Kutta method; time integration; error estimators; Chebyshev methods; algorithm Related Software: RODAS; S-ROCK; RKC; STDTST; NSDTST; Mathematica; MATLAB ODE suite; ode23s; ode113; Ode15s; ode45; ode23; Matlab; CVODE; IRKC Referenced in: 7 Publications all top 5 Referenced by 12 Authors 3 Abdulle, Assyr 2 Vilmart, Gilles 1 Almuslimani, Ibrahim 1 Blumenthal, Adrian 1 Bocher, Philippe 1 Carpenter, Mark H. 1 Huber, Martin E. 1 Kennedy, Christopher A. 1 Montijano, Juan Ignacio 1 O’Sullivan, Stephen 1 Rández, Luis 1 Van Daele, Marnix Referenced in 5 Serials 3 Journal of Computational Physics 1 Numerische Mathematik 1 Applied Numerical Mathematics 1 Journal of Scientific Computing 1 SIAM Journal on Scientific Computing all top 5 Referenced in 6 Fields 7 Numerical analysis (65-XX) 2 Partial differential equations (35-XX) 2 Probability theory and stochastic processes (60-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX) Referencing Publications by Year