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

下载

页码：192 / 208

页数：17

共 50 条

[11] POLYNOMIAL CHAOS IN STOCHASTIC FINITE-ELEMENTS
GHANEM, R
SPANOS, PD
JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME, 1990, 57 (01): : 197 - 202
[12] Comparison of finite difference and finite element solutions to the variably saturated flow equation
Simpson, MJ
Clement, TP
JOURNAL OF HYDROLOGY, 2003, 270 (1-2) : 49 - 64
[13] COMPARISON OF SOME FINITE ELEMENT AND FINITE DIFFERENCE METHODS FOR A SIMPLE SLOSHING PROBLEM
CHU, W
AIAA JOURNAL, 1971, 9 (10) : 2094 - &
[14] Comparison of finite difference, finite element and boundary element methods for electrostatic charged particle optics
Cubric, D
Lencova, B
Read, FH
ELECTRON MICROSCOPY AND ANALYSIS 1997, 1997, (153): : 91 - 94
[15] Stochastic finite element analysis using polynomial chaos on a flexible rotor with contact nonlinearity
Kartheek, Amaroju
Vijayan, Kiran
NONLINEAR DYNAMICS, 2024, 112 (13) : 11299 - 11311
[16] FINITE-DIFFERENCE AND FINITE-ELEMENT METHODS
MORTON, KW
COMPUTER PHYSICS COMMUNICATIONS, 1976, 12 (01) : 99 - 108
[17] Finite difference methods for stochastic Helmholtz equation driven by white noise
Cui, Yanzhen
Tang, Shibing
Zhang, Chao
Journal of Computational and Applied Mathematics, 2025, 457
[18] Comparison of finite difference and mixed finite element methods for perfectly matched layer models
Bokil, V. A.
Buksas, M. W.
COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2007, 2 (04) : 806 - 826
[19] Finite difference/Galerkin finite element methods for a fractional heat conduction-transfer equation
Li, Can
Li, Min-Min
Sun, Xiaorui
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 44 (10) : 8302 - 8321
[20] A comparison of the finite-difference and the finite-element methods for simulating unstable displacements
Khataniar, Santanu
Peters, Ekwere J.
JOURNAL OF PETROLEUM SCIENCE AND ENGINEERING, 1991, 5 (03) : 205 - 218

← 1 2 3 4 5 →