A Numerical Comparison of Finite Difference and Finite Element Methods for a Stochastic Differential Equation with Polynomial Chaos
Year: 2015
East Asian Journal on Applied Mathematics, Vol. 5 (2015), Iss. 2 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.250714.020515a
East Asian Journal on Applied Mathematics, Vol. 5 (2015), Iss. 2 : pp. 192–208
Published online: 2015-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Stochastic differential equation polynomial chaos finite difference method finite element method non-negative solution.
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Generalized polynomial chaos for the convection diffusion equation with uncertainty
Li, Ning
Zhao, Jianping
Feng, Xinlong
Gui, Dongwei
International Journal of Heat and Mass Transfer, Vol. 97 (2016), Iss. P.289
https://doi.org/10.1016/j.ijheatmasstransfer.2016.02.006 [Citations: 13]