Optimization of Functional Integral Equations: A Spectral Approach

The spectral method of Elnagar and Kazemi (J. Comp. Appl. Math. 76(1-2):147-158, 1996), which yields spectral convergence rate for the approximate solutions of Volterra-Hammerstein integral equations, is generalized in order to solve the larger class of functional integral equation control systems with spectral accuracy. The proposed method is based on the idea of relating spectrally constructed grid points to the structure of projection operators. These operators will be used to approximate the control vector and the associated state vector. Numerical examples are included to demonstrate the accuracy of the proposed method.