full
search.png

Search

close.png

Cancel

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

H. Schurz & K. R. Schneider

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

Published online: 2006-03

Preview Purchase PDF 1800 21088

Cited by

google scholar semantic scholar
Export citation
  • 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.

  • Keywords

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

  • AMS Subject Headings

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

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@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 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 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://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 and K. R. Schneider. (2006). Waveform Relaxation Methods for Stochastic Differential Equations. International Journal of Numerical Analysis and Modeling. 3 (2). 232-254. doi:
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard