A Unifying Framework for the Derivation and Analysis of Effective Classes of One-step Methods for Odes

نویسنده

  • LUIGI BRUGNANO
چکیده

In this paper, we provide a simple framework to derive and analyse several classes of effective onestep methods. The framework consists in the discretization of a local Fourier expansion of the continuous problem. Different choices of the basis lead to different classes of methods, even though we shall here consider only the case of an orthonormal polynomial basis, from which a large subclass of Runge-Kutta methods can be derived. The obtained results are then applied to prove, in a simplified way, the order and stability properties of Hamiltonian BVMs (HBVMs), a recently introduced class of energy preserving methods for canonical Hamiltonian systems (see [1] and references therein). A few numerical tests with such methods are also included, in order to confirm the effectiveness of the methods.

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تاریخ انتشار 2011