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.
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

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