Article
MSC:
34A45,
34G10,
34K30,
35K90,
41A20,
47D03 | MR 2891304 | Zbl 1249.34169 | DOI: 10.1007/s10492-012-0003-1
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Keywords:
abstract differential equations; semigroups of operators; rational approximations; A-stability
abstract differential equations; semigroups of operators; rational approximations; A-stability
Summary:
Recently, we have developed the necessary and sufficient conditions under which a rational function $F(hA)$ approximates the semigroup of operators $\exp (tA)$ generated by an infinitesimal operator $A$. The present paper extends these results to an inhomogeneous equation $u'(t)=Au(t)+f(t)$.
References:
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[3] Práger, M., Taufer, J., Vitásek, E.: Overimplicit multistep methods. Apl. Math. 18 (1973), 399-421. MR 0366041
[4] Taylor, A. E.: Introduction to Functional Analysis. John Wiley & Sons New York (1958). MR 0098966 | Zbl 0081.10202
[5] Vitásek, E.: Approximate solutions of abstract differential equations. Appl. Math. 52 (2007), 171-183. DOI 10.1007/s10492-007-0008-3 | MR 2305871 | Zbl 1164.34457
[6] Yosida, K.: Functional Analysis. Springer Berlin-Heidelberg-New York (1971). Zbl 0217.16001
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