Parallel Solution of Stiff Ordinary Differential Equations

  • Thomas Rauber
  • Gudula Rünger
Part of the The Springer International Series in Engineering and Computer Science book series (SECS, volume 515)


We consider the parallel solution of stiff ordinary differential equations with implicit Runge-Kutta (RK) methods. In particular, we describe parallel implementations of classical implicitRK methods and parallel implementations of diagonal-implicitly iterated RK (DIIRK) methods which have been especially developed for a parallel execution. DIIRK methods have computational redundancy but provide an additional source of parallelism in the form of independent nonlinear equation systems to be solved in each time step. To compare the runtimes of the parallel RK methods, we apply them to systems of ordinary differential equations resulting from a spatial discretization of partial differential equations. As programming platform, we use a Cray T3E.


Parallel Solution Linear Equation System Iteration Vector Stepsize Control Nonlinear Equation System 
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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Thomas Rauber
    • 1
  • Gudula Rünger
    • 2
  1. 1.Institut für InformatikUniversität Halle-WittenbergHalle (Saale)Germany
  2. 2.Institut für InformatikUniversität LeipzigLeipzigGermany

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