Optimal explicit stabilized integrator of weak order one for stiff and ergodic stochastic differential equations
arXiv:1708.08145 · doi:10.1137/17M1145859
Abstract
A new explicit stabilized scheme of weak order one for stiff and ergodic stochastic differential equations (SDEs) is introduced. In the absence of noise, the new method coincides with the classical deterministic stabilized scheme (or Chebyshev method) for diffusion dominated advection-diffusion problems and it inherits its optimal stability domain size that grows quadratically with the number of internal stages of the method. For mean-square stable stiff stochastic problems, the scheme has an optimal extended mean-square stability domain that grows at the same quadratic rate as the deterministic stability domain size in contrast to known existing methods for stiff SDEs [A. Abdulle and T. Li. Commun. Math. Sci., 6(4), 2008, A. Abdulle, G. Vilmart, and K. C. Zygalakis, SIAM J. Sci. Comput., 35(4), 2013]. Combined with postprocessing techniques, the new methods achieve a convergence rate of order two for sampling the invariant measure of a class of ergodic SDEs, achieving a stabilized version of the non-Markovian scheme introduced in [B. Leimkuhler, C. Matthews, and M. V. Tretyakov, Proc. R. Soc. A, 470, 2014].
References in corpus (2)
Cited by in corpus (7)
- Explicit stabilized integrators for stiff optimal control problems
- Mixed-precision explicit stabilized Runge-Kutta methods for single- and multi-scale differential equations
- Convergence analysis of explicit stabilized integrators for parabolic semilinear stochastic PDEs
- Conservative stabilized Runge-Kutta methods for the Vlasov-Fokker-Planck equation
- Uniformly accurate schemes for drift--oscillatory stochastic differential equations
- Hopf algebra structures for the backward error analysis of ergodic stochastic differential equations
- A fully adaptive explicit stabilized integrator for advection-diffusion-reaction problems