UNIFORMCONVERGENCE OF INTERLACED EULER METHOD FOR STIFF STOCHASTIC DIFFERENTIAL EQUATIONS

作者：Cipcigan Ioana^*; Rathinam Muruhan

来源：Multiscale Modeling and Simulation, 2011, 9(3): 1217-1252.

DOI：10.1137/080743305

• stochastic differential equations
• stiffness
• uniform convergence
• implicit methods
• Euler methods
• absolute stability

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 convergence with respect to the time scale separation parameter e is a desirable property of a stiff solver. We prove that the means and variances of this interlaced method converge uniformly in e for a suitably chosen test problem. We also illustrate the effectiveness of this method via some numerical examples.

• 出版日期2011