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APPLICATION DE LA METHODE DE COLLOCATION RBF POUR LA RESOLUTION DE CERTAINES EQUATIONS AUX DERIVEES PARTIELLES

Abstract : We have in this work tested successfully the RBF method on the stiff problem, the problem of the concentration of a contaminating, the model Black-Scholes and the model of the classic field of a meson. Our contribution was important during the resolution of the nonlinear equation of Klein-Gordon. The convergence and the efficiency of the method was shown thanks to the RMSE between the analytical solution and the numerical solution. The introduction put aside, this thesis was composed of four chapters. The first one expresses the radial interpolant in the basis of the sub-space of interpolating. The second estimates the error of interpolation in particular cases of the radial basis function and provides the best constants in the increase of the error. The third dedicated to the problem of the quasi-interpolation also allowed to establish the existence and the uniqueness of the solution of the classic field of a meson thanks to the theory of semi-groups and to the theorem of the fixed point of Banach. The fourth was dedicated to the numeric applications. A numeric simulation was made for the problem of the concentration of a contaminating. We finished by a conclusion and perspectives by appointing the future research lines on the topic.
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https://tel.archives-ouvertes.fr/tel-00125243
Contributor : Antoine Filankembo Ouassissou <>
Submitted on : Thursday, January 18, 2007 - 3:28:11 PM
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Antoine Filankembo Ouassissou. APPLICATION DE LA METHODE DE COLLOCATION RBF POUR LA RESOLUTION DE CERTAINES EQUATIONS AUX DERIVEES PARTIELLES. Mathématiques [math]. Université de Pau et des Pays de l'Adour, 2006. Français. ⟨tel-00125243⟩

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