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A Numerical Comparison of Finite Difference and Finite Element Methods for a Stochastic Differential Equation with Polynomial Chaos

Published online by Cambridge University Press:  28 May 2015

Ning Li ,
Bo Meng ,
Xinlong Feng  and
Dongwei Gui
Ning Li
Affiliation:
College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, P.R. China
Bo Meng
Affiliation:
College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, P.R. China
Xinlong Feng
Affiliation:
College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, P.R. China
Dongwei Gui*
Affiliation:
State Key Laboratory of Desert and Oasis Ecology, Xinjiang Institute of Ecology and Geography, Chinese Academy of Sciences, Urumqi 830001; Cele National Station of Observation & Research for Desert-Grassland Ecosystem in Xinjiang, Cele 848300, Xinjiang, P.R. China.
*
*Corresponding author. Email addresses: future_lining@163.com (N. Li), future_bo@163.com (B. Meng), fxlmath@gmail.com (X. Feng), dongwei@ms.xjb.ac.cn (D. Gui)
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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

60H1060H3565L1274S05Stochastic differential equationpolynomial chaosfinite difference methodfinite element methodnon-negative solution
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 5 , Issue 2 , May 2015 , pp. 192 - 208
Copyright
Copyright © Global-Science Press 2015 

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