E. Vitasek, Institute of Mathematics of the Academy of Sciences of the Czech Republic, Zitna 25, 115 67 Praha 1, Czech Republic, e-mail: vitas@math.cas.cz
Abstract: The methods of arbitrarily high orders of accuracy for the solution of an abstract ordinary differential equation are studied. 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.
Keywords: abstract differential equations, semigroups of operators, rational approximations, $A$-stability
Classification (MSC 2000): 34K30, 34G10, 35K90, 47D03
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