Fujiwara’s method can be considered as an extrapolation method of order 6 of the Ninomiya–Victoir weak approximation scheme for the numerical approximation of solution processes of SDEs. We present an extension of Fujiwara’s method for arbitrarily high orders, which embeds the original Fujiwara method as the order 6 case. The approach can be considered as a variant of Richardson extrapolation, which allows one to reach high orders with few extrapolation steps. The most important contribution of our approach is that we only need m extrpolation steps in order to achieve order of approximation 2m, which is half the number of steps in comparison to classical approaches.
"A new extrapolation method for weak approximation schemes with applications." Ann. Appl. Probab. 22 (3) 1008 - 1045, June 2012. https://doi.org/10.1214/11-AAP774