Geodesic
Approximate solutions of abstract differential equations
Applications of Mathematics, Tome 52 (2007) no. 2, pp. 171-183.

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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.
DOI : 10.1007/s10492-007-0008-3
Classification : 34G10, 34K30, 35K90, 47D03
Keywords: abstract differential equations; semigroups of operators; rational approximations; $A$-stability 
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Vitásek, Emil. Approximate solutions of abstract differential equations. Applications of Mathematics, Tome 52 (2007) no. 2, pp. 171-183. doi : 10.1007/s10492-007-0008-3. http://geodesic.mathdoc.fr/articles/10.1007/s10492-007-0008-3/

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