Finite modeling of parabolic equations using Galerkin methods and inverse matrix approximations

In this paper we examine order reduction of parabolic systems using modal truncation. The parabolic distributed system is first approximated using the Galerkin method. The system matrices have a special structure that allows us to find the approximate spectrum of the parabolic system. To do this we compute approximate inverses of tridiagonal, diagonally dominant symmetric matrices. The approximation leads to algorithms of orderO(n), as opposed to traditional algorithms of orderO(n), wheren is the order of the system. Finally, an example is presented to illustrate the proposed algorithm.This research was supported by the National Science Foundation under contract NCR-9210408, by the Advanced Research Programs Agency under contract MDA-972-93-1-0032, and by the University of Hawaii Research Council Funds.