## 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 |

Cited in: | 7 Publications |

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### Cited by 12 Authors

### Cited 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 |

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