抄録
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.
