Approximate solutions of abstract differential equations |
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Authors: | Emil Vitásek |
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Institution: | (1) Institute of Mathematics of the Academy of Sciences of the Czech Republic Žitná 25, 115 67 Praha 1, Czech Republic |
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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.
The research was supported by the Academy of Sciences of the Czech Republic, Institutional Research Plan No. AV0Z10190503. |
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Keywords: | abstract differential equations semigroups of operators rational approximations A-stability |
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