A numerical method for high order approximation of
u(
t)=exp (
tA)
u0, where
A is an
N×
N matrix and
u0 is an
N dimensional vector, based on the continued fraction expansion of exp
z is given. The approximants
Hk(
z) of the continued fraction expansion of exp
z are shown to satisfy
|Hk(
z)
|≤1 for Re
z≤0, which results in an unconditionally stable method when every eigenvalue of
A lies in the left half-plane or on the imaginary axis.
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