Scholarly Communications Project

Solution Representation and Identification for Singular Neutral Functional Differential Equations

by

Graciela M. Cerezo

Dissertation submitted to the Faculty of the Virginia Tech in partial fulfillment of the requirements for the degree of

Ph. D. in Mathematics

in

Mathematics

Approved

Terry L. Herdman, Chair
John A. Burns
Jeffrey Borggaard
David L. Russell
Eugene M. Cliff

December 6, 1996
Blacksburg, Virginia

Abstract

The solutions for a class of Neutral Functional Differential 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 approximations 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.

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