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unconditional stability; complex Banach space; finite difference method; $k$-step formula

References:

[1] I. Babuška M.Práger, E. Vitásek: **Numerical Processes in Differential Equations**. SNTL, Prague, 1966. MR 0223101 | Zbl 0156.16003

[2] B. L. Ehle: **A-stable Methods and Pade Approximations to the Exponential**. SIAM J. Math. Anal., Vol. 4 (1973), No. 4, pp. 671-680. DOI 10.1137/0504057 | MR 0331787 | Zbl 0236.65016

[3] A. Iserles: **On the A-acceptability of Pade Approximations**. SIAM J. Math. Anal., Vol. 10 (1979), No. 5, pp. 1002-1007. DOI 10.1137/0510091 | MR 0541096 | Zbl 0441.41010

[4] E. Hille, R. S. Phillips: **Functional Analysis and Semi-groups**. Amer. Math. Soc., Vol. 31., rev. ed., Waverly Press, Baltimore, 1957. MR 0089373