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AbstractBackgroundMain resultThe Runge–Kutta methodNumerical ExampleRecent developmentsAppendix/BackupL R ((A))-valued random variablesApproximation theoremThe AlgorithmsMain tools (Theorem 2):For the RHS of (2)Let A 0 = {v 0 , v 1 v 1 , v 2 v 2 ,...,v d v d }⊂A ∗ .Then⎛⎞exp ⎜⎝ v 0 + 1 d∑ ∑v 2 i2⎟⎠ =1i=1 w=w 1···w l2 |w|−l l! w,w 1 ,...,w l ∈A 0that is,⎧1 ⎪⎨ if w ∈ A 0C(w) =2⎪⎩|w|−l l!0 otherwise.(4)S. Ninomiya, M. Ninomiya Extension of a higher-order weak approximation
AbstractBackgroundMain resultThe Runge–Kutta methodNumerical ExampleRecent developmentsAppendix/BackupL R ((A))-valued random variablesApproximation theoremThe AlgorithmsAlgebraic relations between {c j } { }Mj=1 , R ij1≤i≤j≤MUsing following 3 results, the algebraic relations are obtained.S. Ninomiya, M. Ninomiya Extension of a higher-order weak approximation
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