Localized solutions for the finite difference semi-discretization of the wave equation
نویسندگان
چکیده
منابع مشابه
Asymptotic Behavior of Solutions to the Finite-Difference Wave Equation
where up in Eq. (2) corresponds to u(jôx, not) in Eq. (1), and where a = cSt/Sx. Here öt and Sx are the time and space intervals, respectively. We consider the case — co < x < », í > 0. It was shown by Courant, Friedrichs, and Lewy in a wellknown paper [1] that if up and u,x are prescribed for ally, then the computational process represented by Eq. (2) will yield values for w/ which converge to...
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In this paper we consider a system of two coupled conservative wave equations and we prove an observability estimate. We treat the question of uniform observability for the finite difference semi-discretization. As for a single wave equation (see Infante and Zuazua (Math. Model. Num. Ann. 33, 407–438, 1999)), we prove that there exists a lack of numerical observability, i.e., the constant on th...
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ژورنال
عنوان ژورنال: Comptes Rendus Mathematique
سال: 2010
ISSN: 1631-073X
DOI: 10.1016/j.crma.2010.03.020