Projection methods for stochastic differential equations with conserved quantities

被引：19

作者：

Zhou, Weien ^{[1
]}

Zhang, Liying ^{[2
]}

Hong, Jialin ^{[3
]}

Song, Songhe ^{[1
,4
]}

机构：

[1] Natl Univ Def Technol, Coll Sci, Changsha 410073, Hunan, Peoples R China

[2] China Univ Min & Technol, Sch Math Sci, Beijing 100083, Peoples R China

[3] Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China

[4] Natl Univ Def Technol, State Key Lab High Performance Comp, Changsha 410073, Hunan, Peoples R China

来源：

BIT NUMERICAL MATHEMATICS | 2016年 / 56卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Stochastic differential equations; Conserved quantities; Projection methods; Mean-square convergence; HAMILTONIAN-SYSTEMS; NUMERICAL-METHODS; ADDITIVE NOISE;

D O I：

10.1007/s10543-016-0614-0

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

In this paper, we consider the numerical methods preserving single or multiple conserved quantities, and these methods are able to reach high order of strong convergence simultaneously based on some kinds of projection methods. The mean-square convergence orders of these methods under certain conditions are given, which can reach order 1.5 or even 2 according to the supporting methods embedded in the projection step. Finally, three numerical experiments are taken into account to show the superiority of the projection methods.

引用

页码：1497 / 1518

页数：22

共 19 条

[1]

Anton CA, 2014, INT J NUMER ANAL MOD, V11, P427

[2] Numerical methods for strong solutions of stochastic differential equations: an overview [J].