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On Solution Regularity of Linear Hyperbolic Stochastic PDE Using the Method of Characteristics

Published online by Cambridge University Press:  28 May 2015

Lizao Li
Lizao Li*
Affiliation:
School of Mathematics, University of Minnesota, USA
*
Corresponding author. Email: lixxl445@umn.edu
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Abstract

The generalized Polynomial Chaos (gPC) method is one of the most widely used numerical methods for solving stochastic differential equations. Recently, attempts have been made to extend the the gPC to solve hyperbolic stochastic partial differential equations (SPDE). The convergence rate of the gPC depends on the regularity of the solution. It is shown that the characteristics technique can be used to derive general conditions for regularity of linear hyperbolic PDE, in a detailed case study of a linear wave equation with a random variable coefficient and random initial and boundary data.

Keywords

52B1065D1868U05Hyperbolic equationstochastic PDEsregularitycharacteristic method
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 2 , Issue 3 , August 2012 , pp. 266 - 276
Copyright
Copyright © Global-Science Press 2012

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References

[1]Gottlieb, D. and Xiu, D.. Galerkin method for wave equations with uncertain coefficients. Commun. Comput. Phys., 3(2):505–518, 2008.Google Scholar
[2]Higham, D.. An algorithmic introduction to numerical simulation of stochastic differential equations. SIAM Review, 43(3):525–546, 2001.Google Scholar
[3]Motamed, M., Nobile, F., and Tempone, R.. A stochastic collocation method for the second order wave equation with a discontinuous random speed. MOX Report 36/2011, submitted, 2011.Google Scholar
[4]Serre, D.. Systems of Conservation Laws. Cambridge University Press, 1999.Google Scholar
[5]Tang, T. and Zhou, T.. Convergence analysis for stochastic collocation methods to scalar hyperbolic equations with a random wave speed. Commun. Comput. Phys., 8(1):226–248, Feb 2010.Google Scholar
[6]Xiu, D.. Fast numerical methods for stochastic computations: A review. Commun. Comput. Phys., 5(2-4):242–272, Feb 2009.Google Scholar