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AbstractBackgroundMain resultThe Runge–Kutta methodNumerical ExampleRecent developmentsAppendix/BackupBoth approaches are necessary because:◮ PDE approach works only when◮◮L is elliptic,dimesion is small.◮ Simulation is the last resort but (people believes) very timeconsuming.This presentation focuses on “Simulation.”S. Ninomiya, M. Ninomiya Extension of a higher-order weak approximation