Projection–difference method for controlled Fourier filtering

Abstract

A projection---difference method is developed for approximating controlled Fourier filtering for quasilinear parabolic functional-differential equations. The method relies on a projection---difference scheme (PDS) for the approximation of the differential problem and derives a O(?1/2?+?h) bound on the rate of convergence of PDS in the weighted energy norm without prior assumptions of additional smoothness of the generalized solutions. The PDS leads to a natural approximation of the objective functional in the optimal Fourier filtering problem. A bound of the same order is obtained for the rate of convergence in the functional of the problems approximating the Fourier filter control problem.