An Electronic Differential Analyzer

Macnee, Alan B.

doi:10.1109/jrproc.1949.229676

Cited by 26 publications

References 8 publications

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A Mathematical Basis for an Error Analysis of Differential Analyzers

Miller

Murray

1953

Journal of Mathematics and Physics

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1.1. Purpose and Literature. The purpose of this paper is to present a mathematical basis for a general error analysis for the solution of systems of ordinary differential equations by machine methods. Specifically, we shall concern ourselves with the effect of errors on the machme solutions. We show that the study of these effects for general non-linear systems can be referred to the solution of linear systems of ordinary differential equations, but we do this without "linearizing" or simplifying the given system.Since we permit perturbations in the solution as given by the machine, our discussion IS apphcable to both continuous computers and digital machines using step by step methods. However, stability discussions for such a digital process are most conveniently given in terms of difference equations rather than differential equations and are not given here.There , but an intensive analysis of this work is not appropriate here One of our major objectives is to avoid the "linearization" which appears in these and In this sense our results can be regarded as supplementing thIS work.The effect of errors on solutions obtained by means of continuous computers has been studied in the case in which the given problem involves a system of linear equations WIth C01stant coefficients, nota.bly by Raymond [34] and Macnee [27, 28].Our dIscussion is based to a certain extent on well known theories for the dependence of systems of ordmary differential equations on parameters. However, it was necessary to extend this theory m order to properly consider those errors which affect the order of the system. Order variations in systems of equations have been considered from other points of view by Coddington and LeVIn-

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