An Error Analysis of Electronic Analog Computers

Due to the physical unrealizability of electronic adding and integrating circuits with ideal characteristics, errors will be introduced in the solution of differential equations obtained by the use of electrical analog computers. Numerical errors in the solution will be introduced by fluctuations in...

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Bibliographic Details
Published in:IEEE transactions on electronic computers 1956-12, Vol.EC-5 (4), p.207-212
Main Author: Marsocci, Velio A.
Format: Article
Language:English
Subjects:
Analog computers
Circuits
Computer errors
Differential equations
Electron tubes
Error analysis
Fluctuations
Frequency response
Machine components
Voltage
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Summary:Due to the physical unrealizability of electronic adding and integrating circuits with ideal characteristics, errors will be introduced in the solution of differential equations obtained by the use of electrical analog computers. Numerical errors in the solution will be introduced by fluctuations in the value of plate and of grid supply voltages, changes in the values of circuit components, and changes in the values of the vacuum tube constants. In addition, the limited frequency response of the machine components will cause the computer to solve a characteristic equation of a higher order than the original characteristic equation whose solution is desired. The error in the solution manifests itself as a shifting in the roots of the original characteristic equation as well as the production of some extra roots. The effect of this change in the root position as well as the presence of the extra roots is experienced in the curve of the solution as a function of the independent variable. In a paper on the accuracy of differential analyzers, Macnee1 has derived an expression which gives the value of the characteristic root shift. The use of this expression is accurate only for certain types of ordinary differential equations. In this paper a new expression for the value of the root shift is derived. The analysis preceding the new root-shift expression is developed in such a manner as to include the Macnee analysis as a special case.
ISSN:0367-9950
0367-7508
DOI:10.1109/TEC.1956.5219953