Numerical approximation and identification problems for singular neutral equations

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.