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Boundary controllability of the finite-difference space semi-discretizations of the beam equation

Liliana León, Enrique Zuazua (2002)

ESAIM: Control, Optimisation and Calculus of Variations

We propose a finite difference semi-discrete scheme for the approximation of the boundary exact controllability problem of the 1-D beam equation modelling the transversal vibrations of a beam with fixed ends. First of all we show that, due to the high frequency spurious oscillations, the uniform (with respect to the mesh-size) controllability property of the semi-discrete model fails in the natural functional setting. We then prove that there are two ways of restoring the uniform controllability...

Boundary controllability of the finite-difference space semi-discretizations of the beam equation

Liliana León, Enrique Zuazua (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We propose a finite difference semi-discrete scheme for the approximation of the boundary exact controllability problem of the 1-D beam equation modelling the transversal vibrations of a beam with fixed ends. First of all we show that, due to the high frequency spurious oscillations, the uniform (with respect to the mesh-size) controllability property of the semi-discrete model fails in the natural functional setting. We then prove that there are two ways of restoring the uniform controllability...

Boundary value problems for systems of functional differential equations

Tadeusz Jankowski (2002)

Applications of Mathematics

Algorithms for finding an approximate solution of boundary value problems for systems of functional ordinary differential equations are studied. Sufficient conditions for consistency and convergence of these methods are given. In the last section, a construction of methods of arbitrary order is presented.

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