Volume 5, Issue 2
A Numerical Comparison of Finite Difference and Finite Element Methods for a Stochastic Differential Equation with Polynomial Chaos

Ning Li, Bo Meng, Xinlong Feng & Dongwei Gui

East Asian J. Appl. Math., 5 (2015), pp. 192-208.

Published online: 2018-02

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  • Abstract

A numerical comparison of finite difference (FD) and finite element (FE) methods for a stochastic ordinary differential equation is made. The stochastic ordinary differential equation is turned into a set of ordinary differential equations by applying polynomial chaos, and the FD and FE methods are then implemented. The resulting numerical solutions are all non-negative. When orthogonal polynomials are used for either continuous or discrete processes, numerical experiments also show that the FE method is more accurate and efficient than the FD method.

  • Keywords

Stochastic differential equation, polynomial chaos, finite difference method, finite element method, non-negative solution.

  • AMS Subject Headings

60H10, 60H35, 65L12, 74S05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-5-192, author = {}, title = {A Numerical Comparison of Finite Difference and Finite Element Methods for a Stochastic Differential Equation with Polynomial Chaos}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {5}, number = {2}, pages = {192--208}, abstract = {

A numerical comparison of finite difference (FD) and finite element (FE) methods for a stochastic ordinary differential equation is made. The stochastic ordinary differential equation is turned into a set of ordinary differential equations by applying polynomial chaos, and the FD and FE methods are then implemented. The resulting numerical solutions are all non-negative. When orthogonal polynomials are used for either continuous or discrete processes, numerical experiments also show that the FE method is more accurate and efficient than the FD method.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.250714.020515a}, url = {http://global-sci.org/intro/article_detail/eajam/10794.html} }
TY - JOUR T1 - A Numerical Comparison of Finite Difference and Finite Element Methods for a Stochastic Differential Equation with Polynomial Chaos JO - East Asian Journal on Applied Mathematics VL - 2 SP - 192 EP - 208 PY - 2018 DA - 2018/02 SN - 5 DO - http://doi.org/10.4208/eajam.250714.020515a UR - https://global-sci.org/intro/article_detail/eajam/10794.html KW - Stochastic differential equation, polynomial chaos, finite difference method, finite element method, non-negative solution. AB -

A numerical comparison of finite difference (FD) and finite element (FE) methods for a stochastic ordinary differential equation is made. The stochastic ordinary differential equation is turned into a set of ordinary differential equations by applying polynomial chaos, and the FD and FE methods are then implemented. The resulting numerical solutions are all non-negative. When orthogonal polynomials are used for either continuous or discrete processes, numerical experiments also show that the FE method is more accurate and efficient than the FD method.

Ning Li, Bo Meng, Xinlong Feng & Dongwei Gui. (1970). A Numerical Comparison of Finite Difference and Finite Element Methods for a Stochastic Differential Equation with Polynomial Chaos. East Asian Journal on Applied Mathematics. 5 (2). 192-208. doi:10.4208/eajam.250714.020515a
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