Abstract
In this article, we address two issues related to the perturbation method introduced by Zhang and Lu (J Comput Phys 194:773–794, 2004), and applied to solving linear stochastic parabolic PDE. Those issues are the construction of the perturbation series, and its convergence.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Courant, R., Hilbert, D.: Methods of Mathematical Physics. Interscience, New York (1953)
Cramér, H.: Mathematical methods of statistics, Princeton Landmarks in Mathematics. Princeton University Press, Princeton (1999)
Evans, L.C.: Partial Differential Equations. American Mathematical Society, Providence (1998)
Ghanem, R.G., Spanos, P.D.: Stochastic Finite Elements: A Spectral Approach. Springer, New York (1991)
Lenth, K.: Application of a perturbation method to nonlinear stochastic PDEs. PhD dissertation, University of Wyoming, (2013)
Loève, M.: Probability Theory II, Graduate Texts in Mathematics 46. Springer, New York (1978)
Xiu, D.: Numerical Methods for Stochastic Computations: A Spectral Method Approach. Princeton University Press, Princeton (2010)
Zhang, D., Lu, Z.: An efficient, high-order perturbation approach for flow in random porous media via Karhunen-Loève and polynomial expansions. J. Comput. Phys. 194, 773–794 (2004)
Acknowledgments
The authors would like to thank Victor Ginting for suggesting the considered problem.
Author information
Authors and Affiliations
Corresponding author
Additional information
The authors were partially supported by the NEUP program of the Department of Energy.
Rights and permissions
About this article
Cite this article
Estep, D.J., Polyakov, P.L. On a Perturbation Method for Stochastic Parabolic PDE. Commun. Math. Stat. 3, 215–226 (2015). https://doi.org/10.1007/s40304-015-0056-z
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40304-015-0056-z