NDLI: The application of symbolic mathematics to a singular perturbation problem

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The application of symbolic mathematics to a singular perturbation problem

Content Provider	ACM Digital Library
Author	Horowitz, Ellis
Abstract	A basic technique for the numerical solution of ordinary differential equations is to express them as a singular perturbation problem. However, computational studies indicate that the resultant matrix equations which must be solved are often highly ill-conditioned. In this paper a particular singular perturbation problem which was shown to be ill-conditioned using 8 numerical methods is solved by symbolic techniques. These techniques lead both to an analytic proof of the solution plus to the precise knowledge of the asymptotic behavior of the solution vector as it converges. The difficulties encountered in solving the problem symbolically are discussed. Then several conclusions are drawn about the merits of a symbolic versus a numeric approach when applied to the solution of linear systems. Finally some advice and warnings to both the user and the designer of symbol manipulation systems are given concerning their goals and expectations when large matrix equations are to be solved.
Starting Page	816
Ending Page	825
Page Count	10
File Format	PDF
DOI	10.1145/800194.805865
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1972-08-01
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Navier-stokes equations Singular perturbation problem Symbol manipulation Exact solution of linear systems
Content Type	Text
Resource Type	Article

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