A Numerical Method for Solving Control Differential Equations on Digital Computers

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A Numerical Method for Solving Control Differential Equations on Digital Computers

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Journal of the ACM (JACM) archive
Volume 7 , Issue 1 (January 1960) table of contents

Pages: 61 - 68

Year of Publication: 1960

ISSN:0004-5411

Authors

W. H. Anderson	Bendix Aviation Corporation, Mishawaka, Indiana
R. B. Ball	Bendix Aviation Corporation, Mishawaka, Indiana
J. R. Voss	Bendix Aviation Corporation, Mishawaka, Indiana

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 6, Downloads (12 Months): 24, Citation Count: 1

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ABSTRACT

Frequently, as in missile control systems, linear differential equations are simultaneous with nonlinear but slower acting differential equations. The numerical solution of this type of system on a digital computer is significantly speeded up by approximating the forcing functions with polynomials, solving the linear equations exactly, and numerically integrating the nonlinear equations with Milne integration. Automatic interval adjustment is possible by comparing errors in the nonlinear integration. The interval selected is related to the shortest time constant of the nonlinear equations rather than the shortest of all the equations. With this system, both detailed transient response and steady state conditions are revealed with a minimum of machine time.

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	W. E. Milne , R. R. Reynolds, Stability of a Numerical Solution of Differential Equations, Journal of the ACM (JACM), v.6 n.2, p.196-203, April 1959 [doi>10.1145/320964.320976]
	2	Memo from R. B. REDDY to A. G. Carlton, The numerical integration of differential equations containing small time constants, JHU Applied Physics Laboratory, April 6, 1954