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Title: Exponential time-differencing with embedded Runge–Kutta adaptive step control

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.

Authors:
; ;
Publication Date:
OSTI Identifier:
22382164
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 280; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CHAOS THEORY; COMPARATIVE EVALUATIONS; KORTEWEG-DE VRIES EQUATION; RUNGE-KUTTA METHOD; SCALARS; SOLITONS; STABILITY; TWO-DIMENSIONAL CALCULATIONS

Citation Formats

Whalen, P., Brio, M., and Moloney, J.V. Exponential time-differencing with embedded Runge–Kutta adaptive step control. United States: N. p., 2015. Web. doi:10.1016/J.JCP.2014.09.038.
Whalen, P., Brio, M., & Moloney, J.V. Exponential time-differencing with embedded Runge–Kutta adaptive step control. United States. doi:10.1016/J.JCP.2014.09.038.
Whalen, P., Brio, M., and Moloney, J.V. Thu . "Exponential time-differencing with embedded Runge–Kutta adaptive step control". United States. doi:10.1016/J.JCP.2014.09.038.
@article{osti_22382164,
title = {Exponential time-differencing with embedded Runge–Kutta adaptive step control},
author = {Whalen, P. and Brio, M. and Moloney, J.V.},
abstractNote = {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.},
doi = {10.1016/J.JCP.2014.09.038},
journal = {Journal of Computational Physics},
number = ,
volume = 280,
place = {United States},
year = {Thu Jan 01 00:00:00 EST 2015},
month = {Thu Jan 01 00:00:00 EST 2015}
}