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Volume 23, Issue 1
Waveform Relaxation Methods of Nonlinear Integral-Differential-Algebraic Equations

Yao-Lin Jiang

J. Comp. Math., 23 (2005), pp. 49-66.

Published online: 2005-02

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  • Abstract

In this paper we consider continuous-time and discrete-time waveform relaxation methods for general nonlinear integral-differential-algebraic equations. For the continuous-time case we derive the convergence condition of the iterative methods by invoking the spectral theory on the resulting iterative operators. By using the implicit difference forms, namely the backward-differentiation formulae, we also yield the convergence condition of the discrete waveforms. Numerical experiments are provided to illustrate the theoretical work reported here.

  • Keywords

Nonlinear integral-differential-algebraic equations, Waveform relaxation, Parallel solutions, Convergence of iterative methods, Engineering applications.

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COPYRIGHT: © Global Science Press

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@Article{JCM-23-49, author = {Yao-Lin Jiang}, title = {Waveform Relaxation Methods of Nonlinear Integral-Differential-Algebraic Equations}, journal = {Journal of Computational Mathematics}, year = {2005}, volume = {23}, number = {1}, pages = {49--66}, abstract = {

In this paper we consider continuous-time and discrete-time waveform relaxation methods for general nonlinear integral-differential-algebraic equations. For the continuous-time case we derive the convergence condition of the iterative methods by invoking the spectral theory on the resulting iterative operators. By using the implicit difference forms, namely the backward-differentiation formulae, we also yield the convergence condition of the discrete waveforms. Numerical experiments are provided to illustrate the theoretical work reported here.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8795.html} }
TY - JOUR T1 - Waveform Relaxation Methods of Nonlinear Integral-Differential-Algebraic Equations AU - Yao-Lin Jiang JO - Journal of Computational Mathematics VL - 1 SP - 49 EP - 66 PY - 2005 DA - 2005/02 SN - 23 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8795.html KW - Nonlinear integral-differential-algebraic equations, Waveform relaxation, Parallel solutions, Convergence of iterative methods, Engineering applications. AB -

In this paper we consider continuous-time and discrete-time waveform relaxation methods for general nonlinear integral-differential-algebraic equations. For the continuous-time case we derive the convergence condition of the iterative methods by invoking the spectral theory on the resulting iterative operators. By using the implicit difference forms, namely the backward-differentiation formulae, we also yield the convergence condition of the discrete waveforms. Numerical experiments are provided to illustrate the theoretical work reported here.

Yao-Lin Jiang. (2005). Waveform Relaxation Methods of Nonlinear Integral-Differential-Algebraic Equations. Journal of Computational Mathematics. 23 (1). 49-66. doi:
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