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AbstractBackgroundMain resultThe Runge–Kutta methodNumerical ExampleRecent developmentsAppendix/BackupL R ((A))-valued random variablesApproximation theoremThe AlgorithmsTheoremBoth X (Alg.1),n and X (Alg.2),n are of order 2.Recent result by KusuokaIf Q (s) is constructed by X (Alg.1),n or X (Alg.2),n then ∃ C > 0s.t.(P s f) (x) − ( Q (s) f ) (x) = Cs (m+1)/2 + O ( s (m+3)/2)S. Ninomiya, M. Ninomiya Extension of a higher-order weak approximation