Fast time-response algorithm for heat conduction feedback systems using IMN approximants

This paper develops a numerical algorithm for calculating the time-responses of a linear feedback system comprising a finite dimensional controller and a distributed-parameter plant described by a heat conduction equation. By approximating the spatial derivatives of the heat equation with finite differences, the feedback system is represented as a large system of linear differential-algebraic equations (DAEs). The I
_MN
recursions, which are suitable for stiff differential equations, are employed in solving such DAEs. The sparse structure in the associated linear algebraic equations is exploited by developing a special LU-factorization scheme. It is found that the algorithm with the new LU-factorization scheme requires only O(ncirc) arithmetic operations where ncirc is the systempsilas dimension, as opposed to O(ncirc
²
) when there is no sparsity exploitation. Hence, substantial computational economy is further achieved.