# Calculating Muliti-integral Time-Ordering operator

I am trying to solve the time-ordering operator Like this: $S(t)=\mathcal{T}e^{\int_0^tduA(u)\int_0^udvB(v)}S(0)$.

How can I calculate S(t) with minimum error?

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## migrated from mathematica.stackexchange.comJul 19 '14 at 22:05

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Baker–Campbell–Hausdorff formula? Brute-force splitting into sums? Who knows. –  acl Jul 19 '14 at 12:39