Abstract
In the present paper, a class of stochastic Runge-Kutta methods containing the second order stochastic Runge-Kutta scheme due to E. Platen for the weak approximation of Itô stochastic differential equation systems with a multi-dimensional Wiener process is considered. Order 1 and order 2 conditions for the coefficients of explicit stochastic Runge-Kutta methods are solved and the solution space of the possible coefficients is analyzed. A full classification of the coefficients for such stochastic Runge-Kutta schemes of order 1 and two with minimal stage numbers is calculated. Further, within the considered class of stochastic Runge-Kutta schemes coefficients for optimal schemes in the sense that additionally some higher order conditions are fulfilled are presented.
Originalsprache | Englisch |
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Zeitschrift | Mathematics and Computers in Simulation |
Jahrgang | 77 |
Ausgabenummer | 4 |
Seiten (von - bis) | 408-420 |
Seitenumfang | 13 |
ISSN | 0378-4754 |
DOIs | |
Publikationsstatus | Veröffentlicht - 04.04.2008 |