This project involves the study of computational techniques for the approximation and control of systems governed by functional integro-differential equations of neutral type. Such systems arise in the modeling of certain aeroelastic control problems and include many singular integro-differential equations. The approach here is based upon a state-space formulation and makes use of approximation results in functional analytic semigroup theory to analyze the convergence of particular numerical schemes. The main objectives of this project are: (1) Select an "appropriate" state-space for singular neutral functional differential equations (SNFDE) and study the properties of the infinitesimal generator of the solution semigroup associated with the homogeneous SNFDE; (2) Develop a general approximation framework for SNFDEs on the state-space and analyze the convergence properties of semi- discretized (i.e., averaging projections and various spline schemes) and fully-discretized numerical schemes for the approximate solutions to the SNFDE; (3) Develop the duality theory for SNFDEs and discuss control and observation problems. **//
