New S-ROCK methods for stochastic differential equations with commutative noise

Iranian Journal of Numerical Analysis and Optimization

مقاله 6، دوره 9، شماره 1 - شماره پیاپی 15، 2019، صفحه 105-126   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.v9i1.69454

نویسنده

A. Haghighi^*

Razi University, Kermanshah, Iran.

چکیده

The class of strong stochastic Runge–Kutta (SRK) methods for stochas tic differential equations with a commutative noise proposed by R¨ oßler (2010) is considered. Motivated by Komori and Burrage (2013), we design a class of explicit stochastic orthogonal Runge–Kutta Chebyshev (SROCKC2) meth ods of strong order one for the approximation of the solution of Itˆo SDEs with an m-dimensional commutative noise.The mean-square and asymptotic stability analysis of the newly proposed methods applied to a scalar linear test equation with a multiplicative noise is presented. Finally, some numer ical experiments for stochastic models arising in applications are given that confirm the theoretical discussion.

کلیدواژه‌ها

Stochastic differential equations؛ Runge-Kutta methods؛ Stochastic mean square stability؛ Stiff equations؛ Commutative noise

مراجع