Adaptive time-stepping for the strong numerical solution of stochastic differential equations

Autor:	Kenneth R. Jackson, Silvana Ilie, Wayne H. Enright
Rok vydání:	2014
Předmět:	Stochastic partial differential equation Stochastic differential equation Mathematical optimization Applied Mathematics Numerical analysis Richardson extrapolation Milstein method Adaptive stepsize Mathematics Numerical stability Numerical partial differential equations
Zdroj:	Numerical Algorithms. 68:791-812
ISSN:	1572-9265 1017-1398
Popis:	Models based on stochastic differential equations are of high interest today due to their many important practical applications. Thus the need for efficient and accurate numerical methods to approximate their solution. In this paper, we propose several adaptive time-stepping strategies for the strong numerical solution of stochastic differential equations in Ito form, driven by multiple Wiener processes satisfying the commutativity condition. The adaptive schemes are based on I and PI control, and allow arbitrary values of the stepsize. The explicit Milstein method is applied to approximate the solution of the problem and the adaptive implementations are based on estimates of the local error obtained using Richardson extrapolation. Numerical tests on several models arising in applications show that our adaptive time-stepping schemes perform better than the fixed stepsize alternative and an adaptive Brownian tree time-stepping strategy.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::bf35646540de64b06aed19ecc65b2905 https://doi.org/10.1007/s11075-014-9872-6 Zobrazit plný text záznamu Full text from SpringerLink