Volume 3, Issue 2
Waveform Relaxation Methods for Stochastic Differential Equations

Int. J. Numer. Anal. Mod., 3 (2006), pp. 232-254.

Published online: 2006-03

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• Abstract

$L^p$-convergence of waveform relaxation methods (WRMs) for numerical solving of systems of ordinary stochastic differential equations (SDEs) is studied. For this purpose, we convert the problem to an operator equation $X = \Pi X + G$ in a Banach space $\varepsilon$ of $\mathcal{F}_t$-adapted random elements describing the initial- or boundary value problem related to SDEs with weakly coupled, Lipschitz-continuous subsystems. The main convergence result of WRMs for SDEs depends on the spectral radius of a matrix associated to a decomposition of $\Pi$. A generalization to one-sided Lipschitz continuous coefficients and a discussion on the example of singularly perturbed SDEs complete this paper.

65C30, 65L20, 65D30, 34F05, 37H10, 60H10

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@Article{IJNAM-3-232, author = {}, title = {Waveform Relaxation Methods for Stochastic Differential Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2006}, volume = {3}, number = {2}, pages = {232--254}, abstract = {

$L^p$-convergence of waveform relaxation methods (WRMs) for numerical solving of systems of ordinary stochastic differential equations (SDEs) is studied. For this purpose, we convert the problem to an operator equation $X = \Pi X + G$ in a Banach space $\varepsilon$ of $\mathcal{F}_t$-adapted random elements describing the initial- or boundary value problem related to SDEs with weakly coupled, Lipschitz-continuous subsystems. The main convergence result of WRMs for SDEs depends on the spectral radius of a matrix associated to a decomposition of $\Pi$. A generalization to one-sided Lipschitz continuous coefficients and a discussion on the example of singularly perturbed SDEs complete this paper.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/898.html} }
TY - JOUR T1 - Waveform Relaxation Methods for Stochastic Differential Equations JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 232 EP - 254 PY - 2006 DA - 2006/03 SN - 3 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/898.html KW - waveform relaxation methods, stochastic differential equations, stochastic-numerical methods, iteration methods, large scale systems. AB -

$L^p$-convergence of waveform relaxation methods (WRMs) for numerical solving of systems of ordinary stochastic differential equations (SDEs) is studied. For this purpose, we convert the problem to an operator equation $X = \Pi X + G$ in a Banach space $\varepsilon$ of $\mathcal{F}_t$-adapted random elements describing the initial- or boundary value problem related to SDEs with weakly coupled, Lipschitz-continuous subsystems. The main convergence result of WRMs for SDEs depends on the spectral radius of a matrix associated to a decomposition of $\Pi$. A generalization to one-sided Lipschitz continuous coefficients and a discussion on the example of singularly perturbed SDEs complete this paper.

H. Schurz & K. R. Schneider. (1970). Waveform Relaxation Methods for Stochastic Differential Equations. International Journal of Numerical Analysis and Modeling. 3 (2). 232-254. doi:
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