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

被引：1

作者：

Li, Ning ^{[1
]}

Meng, Bo ^{[1
]}

Feng, Xinlong ^{[1
]}

Gui, Dongwei ^{[2
,3
]}

机构：

[1] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Peoples R China

[2] Chinese Acad Sci, Xinjiang Inst Ecol & Geog, State Key Lab Desert & Oasis Ecol, Urumqi 830001, Peoples R China

[3] Cele Natl Stn Observat & Res Desert Grassland Eco, Cele 848300, Xinjiang, Peoples R China

来源：

EAST ASIAN JOURNAL ON APPLIED MATHEMATICS | 2015年 / 5卷 / 02期

关键词：

Stochastic differential equation; polynomial chaos; finite difference method; finite element method; non-negative solution; MODELING UNCERTAINTY;

D O I：

10.4208/eajam.250714.020515a

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

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页码：192 / 208

页数：17

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