Výsledky vyhledávání - "Palencia, Cesar"

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Rational methods for abstract linear, non-homogeneous problems without order reduction

Autor: Arranz-Simón, Carlos, Palencia, Cesar

Starting from an A-stable rational approximation to $\rm{e}^z$ of order $p$, $$r(z)= 1+ z+ \cdots + z^p/ p! + O(z^{p+1}),$$ families of stable methods are proposed to time discretize abstract IVP's of the type $u'(t) = A u(t) + f(t)$. These numerical

Externí odkaz: http://arxiv.org/abs/2405.04195

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The numerical range as a spectral set

Autor: Crouzeix, Michel, Palencia, César

It is shown that the numerical range of a linear operator operator in a Hilbert space is a (complete) $(1{+}\sqrt2)$-spectral set. The proof relies, among other things, in the behavior of the Cauchy transform of the conjugates of holomorphic function

Externí odkaz: http://arxiv.org/abs/1702.00668

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Fast Runge-Kutta approximation of inhomogeneous parabolic equations

Autor: López-Fernández, María, Lubich, Christian, Palencia, Cesar, Schädle, Achim

Publikováno v: Numer. Math., Vol. 102, (2), 277 - 291, (2005)

The result after $N$ steps of an implicit Runge-Kutta time discretization of an inhomogeneous linear parabolic differential equation is computed, up to accuracy $\epsilon$, by solving only $$O\Big(\log N \log \frac1\epsilon \Big) $$ linear systems of

Externí odkaz: http://arxiv.org/abs/math/0504466

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A spectral order method for inverting sectorial Laplace transforms

Autor: López-Fernández, María, Palencia, Cesar, Schädle, Achim

Publikováno v: SINUM Vol. 44 (3), 1332-1350, 2006

Laplace transforms which admit a holomorphic extension to some sector strictly containing the right half plane and exhibiting a potential behavior are considered. A spectral order, parallelizable method for their numerical inversion is proposed. The

Externí odkaz: http://arxiv.org/abs/math/0504428

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