TY - JOUR
T1 - Spectral collocation and waveform relaxation methods for nonlinear delay partial differential equations
AU - Jackiewicz, Zdzislaw
AU - Zubik-Kowal, B.
N1 - Funding Information:
* Corresponding author. E-mail addresses: jackiewi@math.la.asu.edu (Z. Jackiewicz), zubik@diamond.boisestate.edu (B. Zubik-Kowal). 1 The work of this author was partially supported by the National Science Foundation under grant NSF DMS-9971164.
Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2006/3
Y1 - 2006/3
N2 - We investigate Chebyshev spectral collocation and waveform relaxation methods for nonlinear delay partial differential equations. Waveform relaxation methods allow to replace the system of nonlinear differential equations resulting from the application of spectral collocation methods by a sequence of linear problems which can be effectively integrated in a parallel computing environment by highly stable implicit methods. The effectiveness of this approach is illustrated by numerical experiments on the Hutchinson's equation. The boundedness of waveform relaxation iterations is proved for the Hutchinson's equation. This result is used in the proof of the superlinear convergence of the iterations.
AB - We investigate Chebyshev spectral collocation and waveform relaxation methods for nonlinear delay partial differential equations. Waveform relaxation methods allow to replace the system of nonlinear differential equations resulting from the application of spectral collocation methods by a sequence of linear problems which can be effectively integrated in a parallel computing environment by highly stable implicit methods. The effectiveness of this approach is illustrated by numerical experiments on the Hutchinson's equation. The boundedness of waveform relaxation iterations is proved for the Hutchinson's equation. This result is used in the proof of the superlinear convergence of the iterations.
KW - Nonlinear partial delay differential equations
KW - Pseudospectral methods
KW - Waveform relaxation iterations
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U2 - 10.1016/j.apnum.2005.04.021
DO - 10.1016/j.apnum.2005.04.021
M3 - Article
AN - SCOPUS:33644611325
SN - 0168-9274
VL - 56
SP - 433
EP - 443
JO - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
IS - 3-4 SPEC. ISS.
ER -