Abstract
In this paper we study the numerical solution of the differential/algebraic systems F(t, y, y′) = 0. Many of these systems can be solved conveniently and economically using a range of ODE methods. Others can be solved only by a small subset of ODE methods, and still others present insurmountable difficulty for all current ODE methods. We examine the first two groups of problems and indicate which methods we believe to be best for them. Then we explore the properties of the third group which cause the methods to fail.
The important factor which determines the solvability of systems of linear problems is a quantity called the global nilpotency. This differs from the usual nilpotency for matrix pencils when the problem is time dependent, so that techniques based on matrix transformations are unlikely to be successful.
Supported in part by the U.S. Department of Energy, Grant DEAC0276ER02383 and by the U.S. Department of Energy Office of Basic Energy Sciences.
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© 1983 Springer-Verlag
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Gear, C.W., Petzold, L.R. (1983). Differential/algebraic systems and matrix pencils. In: Kågström, B., Ruhe, A. (eds) Matrix Pencils. Lecture Notes in Mathematics, vol 973. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062095
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DOI: https://doi.org/10.1007/BFb0062095
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