Exponential time-differencing with embedded Runge-Kutta adaptive step control

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We have presented the first embedded Runge-Kutta exponential time-differencing (RKETD) methods of fourth order with third order embedding and fifth order with third order embedding for non-Rosenbrock type nonlinear systems. A procedure for constructing RKETD methods that accounts for both order conditions and stability is outlined. In our stability analysis, the fast time scale is represented by a full linear operator in contrast to particular scalar cases considered before. An effective time-stepping strategy based on reducing both ETD function evaluations and rejected steps is described. Comparisons of performance with adaptive-stepping integrating factor (IF) are carried out on a set of canonical partial differential equations: the shock-fronts of Burgers equation, interacting KdV solitons, KS controlled chaos, and critical collapse of two-dimensional NLS.

Original languageEnglish (US)
Pages (from-to)579-601
Number of pages23
JournalJournal of Computational Physics
Volume280
DOIs
StatePublished - Jan 1 2015

Fingerprint

Function evaluation
Solitons
Chaos theory
embedding
Partial differential equations
Nonlinear systems
linear operators
Burger equation
shock fronts
nonlinear systems
partial differential equations
chaos
solitary waves
scalars
evaluation

Keywords

  • Burgers
  • Embedded Runge-Kutta
  • ETD
  • Exponential time-differencing
  • KdV
  • NLS

ASJC Scopus subject areas

  • Computer Science Applications
  • Physics and Astronomy (miscellaneous)

Cite this

Exponential time-differencing with embedded Runge-Kutta adaptive step control. / Whalen, P.; Brio, Moysey; Moloney, Jerome V.

In: Journal of Computational Physics, Vol. 280, 01.01.2015, p. 579-601.

Research output: Contribution to journalArticle

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