A differentially algebraic elimination theorem with application to analog computability in the calculus of variations

Authors:
Lee A. Rubel and Michael F. Singer

Journal:
Proc. Amer. Math. Soc. **94** (1985), 653-658

MSC:
Primary 12H05

MathSciNet review:
792278

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Abstract | References | Similar Articles | Additional Information

Abstract: An elimination theorem is proved in differential algebra, from which it follows that an analytic solution of virtually any ordinary differential equation that you can "write down" must actually solve an algebraic differential equation. As a corollary, it follows that the solutions of a large class of variational problems can be produced by an analog computer.

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DOI:
https://doi.org/10.1090/S0002-9939-1985-0792278-1

Article copyright:
© Copyright 1985
American Mathematical Society