High Weak Order Methods for Stochastic Differential Equations Based on Modified Equations

@article{Abdulle2012HighWO,
  title={High Weak Order Methods for Stochastic Differential Equations Based on Modified Equations},
  author={Assyr Abdulle and David Cohen and Gilles Vilmart and Konstantinos C. Zygalakis},
  journal={SIAM J. Scientific Computing},
  year={2012},
  volume={34}
}
Inspired by recent advances in the theory of modified differential equations, we propose a new methodology for constructing numerical integrators with high weak order for the time integration of stochastic differential equations. This approach is illustrated with the constructions of new methods of weak order two, in particular, semi-implicit integrators well suited for stiff (mean-square stable) stochastic problems, and implicit integrators that exactly conserve all quadratic first integrals… CONTINUE READING
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