Volume 2, Issue 3
On Solution Regularity of Linear Hyperbolic Stochastic PDE Using the Method of Characteristics

Lizao Li

East Asian J. Appl. Math., 2 (2012), pp. 266-276.

Published online: 2018-02

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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

Hyperbolic equation stochastic PDEs regularity characteristic method

  • AMS Subject Headings

52B10 65D18 68U05

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COPYRIGHT: © Global Science Press

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@Article{EAJAM-2-266, author = {Lizao Li}, title = {On Solution Regularity of Linear Hyperbolic Stochastic PDE Using the Method of Characteristics}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {2}, number = {3}, pages = {266--276}, 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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.270312.150812a}, url = {http://global-sci.org/intro/article_detail/eajam/10876.html} }
TY - JOUR T1 - On Solution Regularity of Linear Hyperbolic Stochastic PDE Using the Method of Characteristics AU - Lizao Li JO - East Asian Journal on Applied Mathematics VL - 3 SP - 266 EP - 276 PY - 2018 DA - 2018/02 SN - 2 DO - http://doi.org/10.4208/eajam.270312.150812a UR - https://global-sci.org/intro/article_detail/eajam/10876.html KW - Hyperbolic equation KW - stochastic PDEs KW - regularity KW - characteristic method AB -

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.

Lizao Li. (1970). On Solution Regularity of Linear Hyperbolic Stochastic PDE Using the Method of Characteristics. East Asian Journal on Applied Mathematics. 2 (3). 266-276. doi:10.4208/eajam.270312.150812a
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