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Lie-Trotter splitting commutator error
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For bounded matrices,
e
k
B
e
k
C
=
e
k
(
B
+
C
)
+
2
k
2
(
BC
−
CB
)
+
O
(
k
3
)
.
(144)
Commutativity removes this splitting error, though first-order substeps such as backward Euler retain their own quadratic local errors.
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