S-ROCK methods for stochastic delay differential equations with one fixed delay
نویسندگان
چکیده
منابع مشابه
Computational Method for Fractional-Order Stochastic Delay Differential Equations
Dynamic systems in many branches of science and industry are often perturbed by various types of environmental noise. Analysis of this class of models are very popular among researchers. In this paper, we present a method for approximating solution of fractional-order stochastic delay differential equations driven by Brownian motion. The fractional derivatives are considered in the Caputo sense...
متن کاملS-ROCK: Chebyshev Methods for Stiff Stochastic Differential Equations
We present and analyze a new class of numerical methods for the solution of stiff stochastic differential equations (SDEs). These methods, called S-ROCK (for stochastic orthogonal Runge–Kutta Chebyshev), are explicit and of strong order 1 and possess large stability domains in the mean-square sense. For mean-square stable stiff SDEs, they are much more efficient than the standard explicit metho...
متن کاملMulti - step Maruyama methods for stochastic delay differential equations ∗
In this paper the numerical approximation of solutions of Itô stochastic delay differential equations is considered. We construct stochastic linear multi-step Maruyama methods and develop the fundamental numerical analysis concerning their Lp-consistency, numerical Lp-stability and Lpconvergence. For the special case of two-step Maruyama schemes we derive conditions guaranteeing their mean-squa...
متن کاملMixed Stochastic Delay Differential Equations
where W is a Wiener process, Z is a Hölder continuous process with Hölder exponent greater than 1/2, the coefficients a, b, c depend on the past of the process X . The integral with respect to W is understood in the usual Itô sense, while the one with respect to Z is understood in the pathwise sense. (A precise definition of all objects is given in Section 2.) We will call this equation a mixed...
متن کاملExtended one-step methods for solving delay-differential equations
We discuss extended one-step methods of order three for the numerical solution of delay-differential equations. A convergence theorem and the numerical studies regarding the convergence factor of these methods are given. Also, we investigate the stability properties of these methods. The results of the theoretical studies are illustrated by numerical examples.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2019
ISSN: 0377-0427
DOI: 10.1016/j.cam.2018.12.042