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An exponential time-differencing method for monotonic relaxation systems

Abstract

We present first and second-order accurate exponential time differencing methods for a special class of stiff ODEs, denoted as monotonic relaxation ODEs. Some desirable accuracy and robustness properties of our methods are established. In particular, we prove a strong form of stability denoted as monotonic asymptotic stability, guaranteeing that no overshoots of the equilibrium value are possible. This is motivated by the desire to avoid spurious unphysical values that could crash a large simulation.

We present a simple numerical example, demonstrating the potential for increased accuracy and robustness compared to established Runge-Kutta and exponential methods. Through operator splitting, an application to granular-gas flow is provided.

Category

Academic article

Client

  • Own institution / 16X86304
  • Research Council of Norway (RCN) / 189978

Language

English

Author(s)

Affiliation

  • Norwegian University of Science and Technology
  • SINTEF Energy Research / Gassteknologi
  • University of Stavanger
  • SINTEF Industry / Process Technology

Year

2014

Published in

Applied Numerical Mathematics

ISSN

0168-9274

Volume

80

Page(s)

1 - 21

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