Some mathematical limitations of the general-purpose analog computer

Authors:
Lee A Rubel
Affiliations:
Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, Illinois 61801 U.S.A.
Venue:
Advances in Applied Mathematics
Year:
1988

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Abstract

We prove that the Dirichlet problem on the disc cannot be solved by the general-purpose analog computer, by constructing, on the boundary, a function u"0 that does satisfy an algebraic differential equation, but whose Poisson integral u satisfies no algebraic differential equation on some line segment inside the disc.