Rational approximation schemes for solutions of the first and second order Cauchy problem

Jara, Patricio

doi:10.1090/S0002-9939-09-09891-8

Rational approximation schemes for solutions of the first and second order Cauchy problem
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Proc. Amer. Math. Soc. 137 (2009), 3885-3898 Request permission

Abstract:

The purpose of this paper is to give sharp error estimates for regularized versions of $A$-stable rational approximations of $C$-regularized semigroups such as the Backward Euler and Crank-Nicolson scheme among others. The main tools used are those developed by P. Brenner and V. Thomée for strongly continuous semigroups together with a regularized version of the Hille-Phillips functional calculus.

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