Displaying similar documents to “Approximate solutions of abstract differential equations”

Approximate solution of an inhomogeneous abstract differential equation

Emil Vitásek (2012)

Applications of Mathematics

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Recently, we have developed the necessary and sufficient conditions under which a rational function F ( h A ) approximates the semigroup of operators exp ( t A ) generated by an infinitesimal operator A . The present paper extends these results to an inhomogeneous equation u ' ( t ) = A u ( t ) + f ( t ) .

Shape-preserving properties and asymptotic behaviour of the semigroup generated by the Black-Scholes operator

Antonio Attalienti, Ioan Rasa (2008)

Czechoslovak Mathematical Journal

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The paper is devoted to a careful analysis of the shape-preserving properties of the strongly continuous semigroup generated by a particular second-order differential operator, with particular emphasis on the preservation of higher order convexity and Lipschitz classes. In addition, the asymptotic behaviour of the semigroup is investigated as well. The operator considered is of interest, since it is a unidimensional Black-Scholes operator so that our results provide qualitative information...