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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:
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.
References:
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