Browsing by Author "Cerezo, Graciela M."

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    Numerical approximation and identification problems for singular neutral equations
    Cerezo, Graciela M. (Virginia Tech, 1994-04-25)
    A collocation technique in non-polynomial spline space is presented to approximate solutions of singular neutral functional differential equations (SNFDEs). Using solution representations and general well-posedness results for SNFDEs convergence of the method is shown for a large class of initial data including the case of discontinuous initial function. Using this technique, an identification problem is solved for a particular SNFDE. The technique is also applied to other different examples. Even for the special case in which the initial data is a discontinuous function the identification problem is successfully solved.
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    Solution Representation and Indentification for Singular neutral Functional Differential Equations
    Cerezo, Graciela M. (Virginia Tech, 1996-12-06)
    The solutions for a class of Neutral Functional Di erential Equations (NFDE) with weakly singular kernels are studied. Using singular expansion techniques, a representation of the solution of the NFDE is obtained by studing an associated Volterra Integral Equation. We study the Collocation Method as a projection method for the approximation of solutions for Volterra Integral Equations. Particulary, the possibility of achieving higher order ap- proximations is discussed. Special attention is given to the choice of the projection space and its relation to the smoothness of the approximated solution. Finally, we study the identification problem for a parameter appearing in the weakly singular operator of the NFDE.