Cesáreo González

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This paper is concerned with the time discretization of nonlinear evolution equations. We work in an abstract Banach space setting of analytic semigroups that covers fully nonlinear parabolic initial-boundary value problems with smooth coefficients. We prove convergence of variable stepsize backward Euler discretizations under various smoothness assumptions(More)
We consider a quasilinear parabolic problem u′(t) = Q ( u(t) ) u(t), u(t0) = u0 ∈ D, where Q(w) : D ⊂ X → X, w ∈ W ⊂ X, is a family of sectorial operators in a Banach space X with fixed domain D. This problem is discretized in time by means of a strongly A(θ)-stable, 0 < θ ≤ π/2, Runge–Kutta method. We prove that the resulting discretization is stable,(More)
We consider an abstract time-dependent, linear parabolic problem u′(t) = A(t)u(t), u(t0) = u0, where A(t) : D ⊂ X → X, t ∈ J , is a family of sectorial operators in a Banach space X with time-independent domain D. This problem is discretized in time by means of an A(θ) strongly stable Runge-Kutta method, 0 < θ < π/2. We prove that the resulting(More)
In this paper, we consider an explicit exponential method of classical order two for the time discretisation of quasi-linear parabolic problems. The numerical scheme is based on a Magnus integrator and requires the evaluation of two exponentials per step. Our convergence analysis includes parabolic partial differential equations under a Dirichlet boundary(More)
Explicit exponential integrators based on general linear methods are studied for the time discretization of quasi-linear parabolic initial-boundary value problems. Compared to other exponential integrators encountering rather severe order reductions, in general, the considered class of exponential general linear methods provides the possibility to construct(More)
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