On the parallel implementation of implicit Runge-Kutta methods.

*(English)*Zbl 0664.65068The authors consider implicit Runge-Kutta methods whose associated rational function possesses real poles. The use of such methods was proposed by the first author who showed that these methods are \(A_ 0\)- stable. The aim of this paper is to show that a parallel version of these methods, for a stiff linear initial value problem obtained by semidiscretization of the 1-D heat equation, allow speedups very close to the number of processors available. The core of the problem is to decouple a linear system of equations into separate linear systems that can be handled simultaneously. The numerical results are from experiments on IBM-3081D and CRAY-XMP48 computers. For simplicity a two stage method is considered.

Reviewer: Z.Schneider

##### MSC:

65L05 | Numerical methods for initial value problems involving ordinary differential equations |

65L20 | Stability and convergence of numerical methods for ordinary differential equations |

65M20 | Method of lines for initial value and initial-boundary value problems involving PDEs |

65Y05 | Parallel numerical computation |

34A34 | Nonlinear ordinary differential equations and systems |

34K05 | General theory of functional-differential equations |