A Collocative Variation of the Sinc-Galerkin Method for Second Order Boundary Value Problems

Abstract

Feedback and control systems have been studied by engineers for several years but their more rigorous study mathematically is of more recent vintage. Numerical tests of the systems have tended to use time stepping and, for the discretization of spatial derivatives, the less sophisticated but more readily implemented finite difference and low order finite element schemes. Spectral methods in space, the third major technique, are rarely used despite their high accuracy. In part this can be attributed to the considerable implementation costs of spectral methods. Perhaps more telling is that while there have been short monographs published [2] until just recently a comprehensive text covering the subject was lacking. Canuto, et.al., [1] have finally rectified this omission.