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On the parallel implementation of implicit Runge-Kutta methods. (English) Zbl 0664.65068
The 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

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
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