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Progress Report Number 2 on Contract AFOSR-84-0240.
Rept. for 16 Jul 84-16 Dec 85,
NORTH CAROLINA STATE UNIV AT RALEIGH DEPT OF MATHEMATICS
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Implicit systems of differential equations of the form Ft,y,y 0 naturally arise in many circuit and control problems, economic models, and the solution of partial differential equations by the method of lines. Implicit systems are also called singular, differential-algebraic, semi-state, constrained, and descriptor. The theory is well understood, and numerical codes exist, for index zero, index one, and linear constant coefficient problems. Higher index systems occur in circuit and control problems. The numerical and analytic behavior of such higher index systems is not well understood and is incomplete. It has recently been shown that traditional methods, such as backward differences, need not work on higher index systems. Good characterizations of the solution manifold are often difficult to obtain. This research project is to study the numerical and analytic solution of higher index implicit differential equations. Applications will be made to circuit theory, control theory, and the analysis of numerically ill-conditioned index one systems.
APPROVED FOR PUBLIC RELEASE