Mathematics of Computation

Author(s): C. González; C. Palencia.
Journal: Math. Comp. 69 (2000), 609-628.
MSC (1991): Primary 65M12, 65M15, 65M20, 65L06, 65J10, 65J15
Posted: May 20, 1999
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$\begin{displaymath}u'(t) = Q\big( u(t) \big) u(t), \qquad u(t_0) = u_0 \in \mathcal{D}, \end{displaymath}$

where $Q(w) : \mathcal{D}\subset X \to X$ , $w \in W \subset X$ , is a family of sectorial operators in a Banach space

with fixed domain $\mathcal{D}$ . This problem is discretized in time by means of a strongly A( $\theta$ )-stable, $0 < \theta \le\pi/2$ , Runge-Kutta method. We prove that the resulting discretization is stable, under some natural assumptions on the dependence of

with respect to

. Our results are useful for studying in

norms, $1 \le p \le + \infty$ , many problems arising in applications. Some auxiliary results for time-dependent parabolic problems are also provided.

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C. González
Affiliation: Departamento de Matemática Aplicada y Computación, Universidad de Valladolid, Valladolid, Spain
Email: cesareo@mac.cie.uva.es

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