Stochastic Runge-Kutta Methods with Deterministic High Order for Ordinary Differential Equations

被引：0

作者：

Komori, Yoshio ^{[1
]}

Buckwar, Evelyn ^{[2
,3
]}

机构：

[1] Kyushu Inst Technol, Dept Syst Design & Informat, 680-4 Kawazu, Iizuka, Fukuoka, Japan

[2] Heriot Watt Univ, Maxwell Inst Math Sci, Edinburgh EH1 1HX, Midlothian, Scotland

[3] Heriot Watt Univ, Dept Math, Edinburgh EH1 1HX, Midlothian, Scotland

来源：

NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, VOLS A-C | 2011年 / 1389卷

关键词：

Ito stochastic differential equation; weak approximation; explicit scheme; mean square stability;

D O I：

10.1063/1.3637935

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Our aim is to show that the embedding of deterministic Runge-Kutta methods with higher order than necessary order to achieve a weak order can enrich the properties of stochastic Runge-Kutta methods with respect to not only practical errors but also stability. This will be done through the comparisons between our new schemes and an efficient weak second order scheme with minimized error constant proposed by Debrabant and Rossler (2009).

引用

页数：4

共 12 条

[1] Arnold L., 1974, Stochastic Differential Equations: Theory and Applications
[2] Families of efficient second order Runge-Kutta methods for the weak approximation of Ito stochastic differential equations
Debrabant, Kristian
Roessler, Andreas
[J]. APPLIED NUMERICAL MATHEMATICS, 2009, 59 (3-4) : 582 - 594
[3] Hairer E., 2000, SOLVING ORDINARY DIF, V1
[4] A-stability and stochastic mean-square stability
Higham, DJ
[J]. BIT, 2000, 40 (02): : 404 - 409
[5] Kloeden P. E., 1999, NUMERICAL SOLUION ST, DOI DOI 10.1007/978-3-662-12616-5
[6] Komori Y., 1995, MONTE CARLO METH, V1, P279
[7] Weak second-order stochastic Runge-Kutta methods for non-commutative stochastic differential equations
Komori, Yoshio
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2007, 206 (01) : 158 - 173
[8] Supplement: Efficient weak second order stochastic Runge-Kutta methods for non-commutative Stratonovich stochastic differential equations
Komori, Yoshio
Burrage, Kevin
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2011, 235 (17) : 5326 - 5329
[9] Matsumoto M., 1998, ACM Transactions on Modeling and Computer Simulation, V8, P3, DOI 10.1145/272991.272995
[10] Second order Runge-Kutta methods for Stratonovich stochastic differential equations
Roessler, Andreas
[J]. BIT NUMERICAL MATHEMATICS, 2007, 47 (03) : 657 - 680

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