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Stiff Order Conditions for Exponential Runge–Kutta Methods of Order Five

In: Modeling, Simulation and Optimization of Complex Processes - HPSC 2012

Author

Listed:
  • Vu Thai Luan

    (Universität Innsbruck, Institut für Mathematik)

  • Alexander Ostermann

    (Universität Innsbruck, Institut für Mathematik)

Abstract

Exponential Runge–Kutta methods are tailored for the time discretization of semilinear stiff problems. The actual construction of high-order methods relies on the knowledge of the order conditions, which are available in the literature up to order four. In this short note, we show how the order conditions for methods up to order five are derived; the extension to arbitrary orders will be published elsewhere. Our approach is adapted to stiff problems and allows us to prove high-order convergence results for variable step size implementations, independently of the stiffness of the problem.

Suggested Citation

  • Vu Thai Luan & Alexander Ostermann, 2014. "Stiff Order Conditions for Exponential Runge–Kutta Methods of Order Five," Springer Books, in: Hans Georg Bock & Xuan Phu Hoang & Rolf Rannacher & Johannes P. Schlöder (ed.), Modeling, Simulation and Optimization of Complex Processes - HPSC 2012, edition 127, pages 133-143, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-09063-4_11
    DOI: 10.1007/978-3-319-09063-4_11
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