Waveform Relaxation for Functional-Differential Equations

Authors:
Barbara Zubik-Kowal;Stefan Vandewalle
Affiliations:
-;-
Venue:
SIAM Journal on Scientific Computing
Year:
1999

Citing 0
Cited 13

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On the convergence of iterative methods for general differential--algebraic systems

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Remarks on evaluation of spectral radius of operators arising in WR methods for linear systems of ODEs

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Spectral collocation and waveform relaxation methods for nonlinear delay partial differential equations

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Analytical and numerical stability of neutral delay integro-differential equations and neutral delay partial differential equations

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Convergence analysis of waveform relaxation methods for neutral differential-functional systems

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Remarks on evaluation of spectral radius of operators arising in WR methods for linear systems of ODEs

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Spectral collocation and waveform relaxation methods for nonlinear delay partial differential equations

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Waveform relaxation and comparison methods for multipoint boundary value problems

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Delay dependent estimates for waveform relaxation methods for neutral differential-functional systems

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Waveform relaxation method for stochastic differential equations with constant delay

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Convergence of waveform relaxation methods for neutral delay differential equations

Mathematical and Computer Modelling: An International Journal
Waveform relaxation methods for fractional differential equations with the Caputo derivatives

Journal of Computational and Applied Mathematics

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Abstract

The convergence of waveform relaxation techniques for solving functional-differential equations is studied. New error estimates are derived that hold under linear and nonlinear conditions for the right-hand side of the equation. Sharp error bounds are obtained under generalized time-dependent Lipschitz conditions. The convergence of the waveform method and the quality of the a priori error bounds are illustrated by means of extensive numerical data obtained by applying the method of lines to three partial functional-differential equations.