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The simulation of partial differential equations on the digital differential analyzer

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George ForbesAuthors Info & Claims

ACM '72: Proceedings of the ACM annual conference - Volume 2

Pages 860 - 866

https://doi.org/10.1145/800194.805873

Published: 01 August 1972 Publication History

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Abstract

The mathematical analog involved in the Digital Differential Analyzer, (Digital Analog Computer), requires a different approach to partial differential equations. The usual boundary and initial condition problem becomes a selection of auxiliary partial differential equations and of point starting values for the various partial derivatives of the dependent variable.

The DDA System is not suited for the usual classical method of condition definition. In some special cases the classical approach may be made more general because the ordinary differential equations need not be solved, In such case, assumed separability may be an order higher.

This paper discusses these problems and describes the nature of the generalities involved. It is pointed out that the Digital Differential Analyzer can “solve” the simultaneous case of the common partial differential equations.

References

[1]

Forbes, G.F., Digital Differential Analyzers, 4th Edition, 1957, 200 pages. Published by the author at 15415 Lemarsh Street, Mission Hills, California.

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[2]

Forbes, G.F., The System Analyzer, Vol I, Number 1, 72 pages, 1961, see above.

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[3]

Handel, P. von (ed.) Electronic Computers. 1961, Springer-Verlag Chapter IV, pages 139-209 is an excellent discussion of Digital Differential Analyzers by Hans W. Gschwind.

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[4]

Mayorov, F.V., Electronic Digital Integrating Computers—Digital Differential Analyzers. Translated from the Russian by Scriptor Technica, Inc. (Dr. Jackan Chu, ed.) American Elservier Publishing Co. (New York). Originally published in Moscow in 1962. 375 pages.

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[5]

Forbes, G.F., The System Simulator (Digital Differential Analyzers). Unpublished, available in limited amount from Guidance and Control Systems Division, Litton Industries, 5500 Canoga Avenue, Woodland Hills, California. 44 pages. This is a simplified discussion of DDAs, Publication Number 3731A.

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[6]

Forbes, G.F., An Engineering Simulator, Proceedings of the ACM National Meeting, 1966. Pages 241-255. This is a description of the program permitting use of the IBM 7040 as a DDA.

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Index Terms

The simulation of partial differential equations on the digital differential analyzer
1. Computing methodologies
  1. Modeling and simulation
2. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
      1. Partial differential equations

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ACM '72: Proceedings of the ACM annual conference - Volume 2

August 1972

530 pages

ISBN:9781450374927

DOI:10.1145/800194

Chairman:
John J. Donovan,
Editor:
Rosemary Shields

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

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Published: 01 August 1972

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Two-dimensional differential transform for partial differential equations

Solving partial differential equations by two-dimensional differential transform method

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Sylvester Equations and the numerical solution of partial fractional differential equations

Two-dimensional differential transform for partial differential equations

Solving partial differential equations by two-dimensional differential transform method

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