Two-step Milstein schemes for stochastic differential equations.

Authors :: Tocino, A.
Senosiain, M.
Source :: Numerical Algorithms. Jul2015, Vol. 69 Issue 3, p643-665. 23p.
Publication Year :: 2015
Abstract: A set of conditions on the parameters of stochastic linear two-step schemes for their order 1.0 mean-square convergence are established. Then two-step Milstein schemes are defined and necessary and sufficient conditions for their MS-stability are given. Regions of MS-stability are determined and plotted for Adams-Bashforth, Adams-Moulton and BDF Milstein schemes. Numerical experiments confirming the theoretical results are shown. [ABSTRACT FROM AUTHOR]