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

H. Schurz & K. R. Schneider

DOI:

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

Published online: 2006-03

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  • Abstract

L-p-convergence of wave form 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 epsilon of 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.

  • Keywords

waveform relaxation methods stochastic differential equations stochastic-numerical methods iteration methods large scale systems

  • AMS Subject Headings

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

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-3-232, author = {H. Schurz and K. R. Schneider}, 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 wave form 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 epsilon of 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 AU - H. Schurz & K. R. Schneider JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 232 EP - 254 PY - 2006 DA - 2006/03 SN - 3 DO - http://dor.org/ UR - https://global-sci.org/intro/article_detail/ijnam/898.html KW - waveform relaxation methods KW - stochastic differential equations KW - stochastic-numerical methods KW - iteration methods KW - large scale systems AB - L-p-convergence of wave form 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 epsilon of 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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