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

Vu Thai Luan () and Alexander Ostermann ()
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Vu Thai Luan: Universität Innsbruck, Institut für Mathematik
Alexander Ostermann: Universität Innsbruck, Institut für Mathematik

A chapter in Modeling, Simulation and Optimization of Complex Processes - HPSC 2012, 2014, pp 133-143 from Springer

Abstract: 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.

Keywords: Exponential Runge-Kutta Methods; Variable Step Size Implementation; Stiff Problems; Higher Order Methods; Abstract Parabolic Evolution Equations (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-09063-4_11

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DOI: 10.1007/978-3-319-09063-4_11

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