Predictor-corrector methods of Runge-Kutta type for stochastic differential equations


Autoria(s): Burrage, K.; Tian, T. H.
Contribuinte(s)

M. Gunzburser

Data(s)

01/01/2002

Resumo

In this paper we construct predictor-corrector (PC) methods based on the trivial predictor and stochastic implicit Runge-Kutta (RK) correctors for solving stochastic differential equations. Using the colored rooted tree theory and stochastic B-series, the order condition theorem is derived for constructing stochastic RK methods based on PC implementations. We also present detailed order conditions of the PC methods using stochastic implicit RK correctors with strong global order 1.0 and 1.5. A two-stage implicit RK method with strong global order 1.0 and a four-stage implicit RK method with strong global order 1.5 used as the correctors are constructed in this paper. The mean-square stability properties and numerical results of the PC methods based on these two implicit RK correctors are reported.

Identificador

http://espace.library.uq.edu.au/view/UQ:62831/UQ62831_OA.pdf

http://espace.library.uq.edu.au/view/UQ:62831

Idioma(s)

eng

Publicador

Society for Industrial and Applied Mathematics

Palavras-Chave #Mathematics, Applied #Stochastic Differential Equations #Predictor-corrector Methods #Runge-kutta Methods #Numerical Stability #Initial-value Problems #Order Conditions #Implicit
Tipo

Journal Article