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.