Stiffly accurate Runge-Kutta methods for stiff stochastic differential equations

Kevin Burrage; Tianhai Tian

doi:10.1016/S0010-4655(01)00324-1

Stiffly accurate Runge-Kutta methods for stiff stochastic differential equations

Kevin Burrage, Tianhai Tian

School of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

18 Citations (Scopus)

Abstract

In this paper we discuss implicit methods based on stiffly accurate Runge-Kutta methods and splitting techniques for solving Stratonovich stochastic differential equations (SDEs). Two splitting techniques: the balanced splitting technique and the deterministic splitting technique, are used in this paper. We construct a two-stage implicit Runge-Kutta method with strong order 1.0 which is corrected twice and no update is needed. The stability properties and numerical results show that this approach is suitable for solving stiff SDEs.

Original language	English
Title of host publication	Computer Physics Communications
Subtitle of host publication	Conference on Computational Physics (CCP'2000); Gold Coast, Qld.; Australia; 3 December 2000 through 8 December 2000
Pages	186-190
Number of pages	5
Volume	142
Edition	1-3
DOIs	https://doi.org/10.1016/S0010-4655(01)00324-1
Publication status	Published - 15 Dec 2001
Event	Conference on Computational Physics (CCP'2000) - Gold Coast, Qld., Australia Duration: 3 Dec 2000 → 8 Dec 2000

Publication series

Name	Computer Physics Communications
Publisher	Elsevier
ISSN (Print)	0010-4655

Conference

Conference	Conference on Computational Physics (CCP'2000)
Country/Territory	Australia
City	Gold Coast, Qld.
Period	3/12/00 → 8/12/00

Keywords

Runge-Kutta methods
Stability
Stiff accuracy
Stochastic differential equations

Access to Document

10.1016/S0010-4655(01)00324-1

Cite this

Burrage, K., & Tian, T. (2001). Stiffly accurate Runge-Kutta methods for stiff stochastic differential equations. In Computer Physics Communications: Conference on Computational Physics (CCP'2000); Gold Coast, Qld.; Australia; 3 December 2000 through 8 December 2000 (1-3 ed., Vol. 142, pp. 186-190). (Computer Physics Communications). https://doi.org/10.1016/S0010-4655(01)00324-1

@inproceedings{26aa9cdcb47749efa4689fa9fc323b61,

title = "Stiffly accurate Runge-Kutta methods for stiff stochastic differential equations",

abstract = "In this paper we discuss implicit methods based on stiffly accurate Runge-Kutta methods and splitting techniques for solving Stratonovich stochastic differential equations (SDEs). Two splitting techniques: the balanced splitting technique and the deterministic splitting technique, are used in this paper. We construct a two-stage implicit Runge-Kutta method with strong order 1.0 which is corrected twice and no update is needed. The stability properties and numerical results show that this approach is suitable for solving stiff SDEs.",

keywords = "Runge-Kutta methods, Stability, Stiff accuracy, Stochastic differential equations",

author = "Kevin Burrage and Tianhai Tian",

year = "2001",

month = dec,

day = "15",

doi = "10.1016/S0010-4655(01)00324-1",

language = "English",

volume = "142",

series = "Computer Physics Communications",

publisher = "Elsevier",

pages = "186--190",

booktitle = "Computer Physics Communications",

edition = "1-3",

note = "Conference on Computational Physics (CCP'2000) ; Conference date: 03-12-2000 Through 08-12-2000",

}

Burrage, K & Tian, T 2001, Stiffly accurate Runge-Kutta methods for stiff stochastic differential equations. in Computer Physics Communications: Conference on Computational Physics (CCP'2000); Gold Coast, Qld.; Australia; 3 December 2000 through 8 December 2000. 1-3 edn, vol. 142, Computer Physics Communications, pp. 186-190, Conference on Computational Physics (CCP'2000), Gold Coast, Qld., Australia, 3/12/00. https://doi.org/10.1016/S0010-4655(01)00324-1

Stiffly accurate Runge-Kutta methods for stiff stochastic differential equations. / Burrage, Kevin; Tian, Tianhai.
Computer Physics Communications: Conference on Computational Physics (CCP'2000); Gold Coast, Qld.; Australia; 3 December 2000 through 8 December 2000. Vol. 142 1-3. ed. 2001. p. 186-190 (Computer Physics Communications).

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

TY - GEN

T1 - Stiffly accurate Runge-Kutta methods for stiff stochastic differential equations

AU - Burrage, Kevin

AU - Tian, Tianhai

PY - 2001/12/15

Y1 - 2001/12/15

N2 - In this paper we discuss implicit methods based on stiffly accurate Runge-Kutta methods and splitting techniques for solving Stratonovich stochastic differential equations (SDEs). Two splitting techniques: the balanced splitting technique and the deterministic splitting technique, are used in this paper. We construct a two-stage implicit Runge-Kutta method with strong order 1.0 which is corrected twice and no update is needed. The stability properties and numerical results show that this approach is suitable for solving stiff SDEs.

AB - In this paper we discuss implicit methods based on stiffly accurate Runge-Kutta methods and splitting techniques for solving Stratonovich stochastic differential equations (SDEs). Two splitting techniques: the balanced splitting technique and the deterministic splitting technique, are used in this paper. We construct a two-stage implicit Runge-Kutta method with strong order 1.0 which is corrected twice and no update is needed. The stability properties and numerical results show that this approach is suitable for solving stiff SDEs.

KW - Runge-Kutta methods

KW - Stability

KW - Stiff accuracy

KW - Stochastic differential equations

UR - http://www.scopus.com/inward/record.url?scp=0035892821&partnerID=8YFLogxK

U2 - 10.1016/S0010-4655(01)00324-1

DO - 10.1016/S0010-4655(01)00324-1

M3 - Conference Paper

AN - SCOPUS:0035892821

VL - 142

T3 - Computer Physics Communications

SP - 186

EP - 190

BT - Computer Physics Communications

T2 - Conference on Computational Physics (CCP'2000)

Y2 - 3 December 2000 through 8 December 2000

ER -

Stiffly accurate Runge-Kutta methods for stiff stochastic differential equations

Abstract

Publication series

Conference

Keywords

Access to Document

Other files and links

Cite this