SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Invited Talk

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Weak order exponential Runge-Kutta methods for stiff stochastic differential equations

Y. Komori, D. Cohen and K. Burrage

We are concerned with numerical methods which give weak approximations for stiff Itô SDEs. It is well known that the numerical solution of stiff SDEs leads to a stepsize reduction when explicit methods are used. However, there are some classes of explicit methods that are well suited to solving some types of stiff SDEs. One such class is the class of stochastic orthogonal Runge-Kutta Chebyshev methods [1]. Another suitable class of methods is the class of Local Linearization (LL) methods that reduce to some exponential Runge-Kutta (RK) methods when applied to semilinear ODEs. Mora [3] and Carbonell et al. [2] have proposed weak second order LL methods for SDEs with additive noise. In this talk, we will propose new exponential RK methods which give weak approximations for multi-dimensional, non-commutative SDEs with a semilinear drift term. Their convergence order and stability properties will be confirmed in numerical examples.

[1] A. Abdulle and T. Li, S-ROCK methods for stiff Itô SDEs, Commun. Math. Sci., 6(4) (2008) 845-868.
[2] F. Carbonell, J.C. Jimenez and R.J. Biscay, Weak local linear discretizations for stochastic differential equations: Convergence and numerical schemes, J. Comput. Appl. Math., 197(2) (2006) 578-596.
[3] C.M. Mora, Weak exponential schemes for stochastic differential equations with additive noise, IMA J. Numer. Anal., 25(3) (2005) 486-506.

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