Modal truncation of parabolic equations using the Galerkin method and inverse matrix approximations

Examines system 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 allow the authors to find the approximate spectrum of the parabolic system. To do this the authors compute approximate inverses of tridiagonal, diagonally dominant symmetric matrices. This approximation leads to algorithms of order O(n), as opposed to traditional algorithms of order O(n³), where n is the order of the system. Finally an example is presented to illustrate the proposed algorithm