Effectiveness of Implicit Methods for Stiff Stochastic Differential Equations
نویسندگان
چکیده
In this paper we study the behavior of a family of implicit numerical methods applied to stochastic differential equations with multiple time scales. We show by a combination of analytical arguments and numerical examples that implicit methods in general fail to capture the effective dynamics at the slow time scale. This is due to the fact that such implicit methods cannot correctly capture non-Dirac invariant distributions when the time step size is much larger than the relaxation time of the system. AMS subject classifications: 65L20, 65C30, 37M25
منابع مشابه
On second derivative 3-stage Hermite--Birkhoff--Obrechkoff methods for stiff ODEs: A-stable up to order 10 with variable stepsize
Variable-step (VS) second derivative $k$-step $3$-stage Hermite--Birkhoff--Obrechkoff (HBO) methods of order $p=(k+3)$, denoted by HBO$(p)$ are constructed as a combination of linear $k$-step methods of order $(p-2)$ and a second derivative two-step diagonally implicit $3$-stage Hermite--Birkhoff method of order 5 (DIHB5) for solving stiff ordinary differential equations. The main reason for co...
متن کاملStability of two classes of improved backward Euler methods for stochastic delay differential equations of neutral type
This paper examines stability analysis of two classes of improved backward Euler methods, namely split-step $(theta, lambda)$-backward Euler (SSBE) and semi-implicit $(theta,lambda)$-Euler (SIE) methods, for nonlinear neutral stochastic delay differential equations (NSDDEs). It is proved that the SSBE method with $theta, lambdain(0,1]$ can recover the exponential mean-square stability with some...
متن کاملUniform Convergence of Interlaced Euler Method for Stiff Stochastic Differential Equations
In contrast to stiff deterministic systems of ordinary differential equations, in general, the implicit Euler method for stiff stochastic differential equations is not effective. This paper introduces a new numerical method for stiff differential equations which consists of interlacing large implicit Euler time steps with a sequence of small explicit Euler time steps. We emphasize that uniform ...
متن کاملApplication of the block backward differential formula for numerical solution of Volterra integro-differential equations
In this paper, we consider an implicit block backward differentiation formula (BBDF) for solving Volterra Integro-Differential Equations (VIDEs). The approach given in this paper leads to numerical methods for solving VIDEs which avoid the need for special starting procedures. Convergence order and linear stability properties of the methods are analyzed. Also, methods with extensive stability r...
متن کاملExplicit methods for stiff stochastic differential equations
Multiscale differential equations arise in the modeling of many important problems in the science and engineering. Numerical solvers for such problems have been extensively studied in the deterministic case. Here, we discuss numerical methods for (mean-square stable) stiff stochastic differential equations. Standard explicit methods, as for example the EulerMaruyama method, face severe stepsize...
متن کاملExplicit stabilized integration of stiff determinisitic or stochastic problems
Explicit stabilized methods for stiff ordinary differential equations have a long history. Proposed in the early 1960s and developed during 40 years for the integration of stiff ordinary differential equations, these methods have recently been extended to implicit-explicit or partitioned type methods for advection-diffusion-reaction problems, and to efficient explicit solvers for stiff mean-squ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2000