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Numerical solution of differential equations

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AIEE-IRE '54 (Eastern): Proceedings of the December 8-10, 1954, eastern joint computer conference: Design and application of small digital computers

Pages 58 - 64

https://doi.org/10.1145/1455270.1455285

Published: 08 December 1954 Publication History

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Abstract

The problem of finding solutions to various types of differential equations has intrigued mathematicians from a theoretical point of view for many years. It has also plagued many applied scientists for an equally long period of time. Except for the relatively few equations whose solutions are available in closed form, the best one can do is to obtain approximate solutions.

References

[1]

Numerical Methods in Digital Real Time Simulation, H. J. Gray, Jr. Dissertation in Electrical Engineering, Moore School of Electrical Engineering, University of Pennsylvania, Philadelphia, Pa., June 1953.

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Numerical Methods in Digital Real Time Simulation, H. J. Gray, Jr. Quarterly of Applied Mathematics, Brown University, Providence, R. I., vol. 12, no. 2, July 1954.

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Calculus of Finite Differences (book), L. M. Milne-Thomson. Macmillan and Company, London, England, 1933.

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The Use of Stability Charts in the Synthesis of Numerical Quadrature Methods, H. M. Gurk. Quarterly of Applied Mathematics, Brown University, Providence, R. I.

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A Survey of the Theory of the Boundedness, Stability and Asymptotic Behavior of Solutions of Linear and Non-Linear Differential and Difference Equations, R. Bellman. Office of Naval Research, Department of the Navy, Washington, D. C., January 1949.

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Stability Theory of Differential Equations (book), R. Bellman. McGraw-Hill Book Company, New York, N. Y., 1953.

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Numerical Solution of Differential Equations (book), W. E. Milne. John Wiley and Sons, Inc., New York, N. Y., 1953.

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The Use of Exponential Sums in Step by Step Integration, P. Brock, F. J. Murray. Mathematical Tables and Other Aids to Computation VI, nos 38 and 39, April and July 1952.

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Cited By

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Vivatson ASlemmer W(1962)Comments on "Real-Time Analog-Digital ComputationIRE Transactions on Electronic Computers10.1109/TEC.1962.5219435EC-11:5(707-708)Online publication date: Oct-1962
https://doi.org/10.1109/TEC.1962.5219435
Vivatson ASlemmer W(1962)Comments on "Real-Time Analog-Digital ComputationIRE Transactions on Electronic Computers10.1109/TEC.1962.5219434EC-11:5(707-707)Online publication date: Oct-1962
https://doi.org/10.1109/TEC.1962.5219434
Connelly M(1962)Real-Time Analog-Digital ComputationIEEE Transactions on Electronic Computers10.1109/TEC.1962.5219313EC-11:1(31-41)Online publication date: Feb-1962
https://doi.org/10.1109/TEC.1962.5219313
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Published In

AIEE-IRE '54 (Eastern): Proceedings of the December 8-10, 1954, eastern joint computer conference: Design and application of small digital computers

December 1954

106 pages

ISBN:9781450378550

DOI:10.1145/1455270

Conference Chairs:
C. W. ADAMS
Massachusetts Institute of Technology
,
W. L. MARTIN
Telecomputing Corporation

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Association for Computing Machinery

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Published: 08 December 1954

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Vivatson ASlemmer W(1962)Comments on "Real-Time Analog-Digital ComputationIRE Transactions on Electronic Computers10.1109/TEC.1962.5219435EC-11:5(707-708)Online publication date: Oct-1962
https://doi.org/10.1109/TEC.1962.5219435
Vivatson ASlemmer W(1962)Comments on "Real-Time Analog-Digital ComputationIRE Transactions on Electronic Computers10.1109/TEC.1962.5219434EC-11:5(707-707)Online publication date: Oct-1962
https://doi.org/10.1109/TEC.1962.5219434
Connelly M(1962)Real-Time Analog-Digital ComputationIEEE Transactions on Electronic Computers10.1109/TEC.1962.5219313EC-11:1(31-41)Online publication date: Feb-1962
https://doi.org/10.1109/TEC.1962.5219313
Haynes M(1961)Transient Analysis of Cryotron Networks by Computer SimulationProceedings of the IRE10.1109/JRPROC.1961.28781649:1(245-257)Online publication date: Jan-1961
https://doi.org/10.1109/JRPROC.1961.287816
Gray HWare W(1958)Digital computer solution of differential equations in real timeProceedings of the May 6-8, 1958, western joint computer conference: contrasts in computers10.1145/1457769.1457796(87-92)Online publication date: 6-May-1958
https://dl.acm.org/doi/10.1145/1457769.1457796
Tou J(1957)Digital Compensation for Control and SimulationProceedings of the IRE10.1109/JRPROC.1957.27852945:9(1243-1248)Online publication date: 1957
https://doi.org/10.1109/JRPROC.1957.278529

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Numerical solution of distributed order fractional differential equations

An approximate method for numerical solution of fractional differential equations

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Numerical solution of distributed order fractional differential equations

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The BEM for numerical solution of partial fractional differential equations

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