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Zbl 1164.34457
Vitásek, Emil
Approximate solutions of abstract differential equations. (English)
[J] Appl. Math., Praha 52, No. 2, 171-183 (2007). ISSN 0862-7940; ISSN 1572-9109/e

Summary: We study methods of arbitrarily high orders of accuracy for the solution of an abstract ordinary differential equation. The right-hand side of the differential equation under investigation contains an unbounded operator which is an infinitesimal generator of a strongly continuous semigroup of operators. Necessary and sufficient conditions are found for a rational function to approximate the given semigroup with high accuracy.

MSC 2000:: *34G10 Linear ODE in abstract spaces
47D03 (Semi)groups of linear operators

Keywords: abstract differential equations; semigroups of operators; rational approximations; $A$-stability

Cited in: Zbl 1249.34169

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