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Mathematical experimentation in time-lag modulation

Authors:

Richard Bellman,

June Buell,

Robert KalabaAuthors Info & Claims

Communications of the ACM, Volume 9, Issue 10

Pages 752 - 754

https://doi.org/10.1145/365844.365865

Published: 01 October 1966 Publication History

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Abstract

Equations of the form du/dt = g(u(t), u(h(t))) arise in a number of scientific contexts. The authors point out some interesting properties of the solution of u′(t) = -u(t - 1 - k sin ωt) + sin at. These properties were obtained by means of numerical solution.

References

[1]

BELLMAN, R., AND COOKE, K.L. Differential-difference Equations. Academic Press Inc., New York, 1963.

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[2]

MYSKIS, A. D. Linear Differential Equations with a Delayed Argument. Gos. Izd. Tekhniko-teoret. Lit., Moscow, 1951.

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[3]

BELLMAN, m., JACQUEZ, J., AND KALABA, R. Mathematical models of chemotherapy. Proc. Fourth Berkeley Symposium on Mathematical Statistics and Probability. Vol. IV. U. of California Press, Berkeley, Calif. 1961, pp. 57-66.

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[4]

BUELL, J., AND GRODINS, F. Model for the Control of Respiration. To appear.

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[5]

BELLMAN, R., AND COOKE, K. L. On the computational solution of a class of functional differential equations. RM-4287-PR, The RAND Corp., Santa Monica, Calif., Oct. 1964.

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BELLMAN, R. On the computational solution of differentialdifference equations, J. Math. Anal. Appl. 2 (1961), 108-110.

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[7]

BELLMAN, R., BUELL, J., AND KALAEA, R. Numerical integration of a differential-difference equation with a decreasing time-lag. Comm. ACM 8, 4(April 1965), 227-228.

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Gurioli GWang WYan X(2024)Hamiltonian Boundary Value Methods (HBVMs) for functional differential equations with piecewise continuous argumentsNumerical Algorithms10.1007/s11075-024-01994-7Online publication date: 13-Dec-2024
https://doi.org/10.1007/s11075-024-01994-7
Baker CPaul CWillé D(2023)Issues in the numerical solution of evolutionary delay differential equationsAdvances in Computational Mathematics10.1007/BF029886253:1(171-196)Online publication date: 22-Mar-2023
https://dl.acm.org/doi/10.1007/BF02988625
Farhloul MFortin M(2023)A mixed finite element for the stokes problem using quadrilateral elementsAdvances in Computational Mathematics10.1007/BF024319983:1-2(101-113)Online publication date: 22-Mar-2023
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Mathematical experimentation in time-lag modulation
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
2. Theory of computation

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Communications of the ACM Volume 9, Issue 10

Oct. 1966

51 pages

ISSN:0001-0782

EISSN:1557-7317

DOI:10.1145/365844

Editor:
Gerard Salton
Cornell Univ., Ithaca, NY

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Association for Computing Machinery

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Publication History

Published: 01 October 1966

Published in CACM Volume 9, Issue 10

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Gurioli GWang WYan X(2024)Hamiltonian Boundary Value Methods (HBVMs) for functional differential equations with piecewise continuous argumentsNumerical Algorithms10.1007/s11075-024-01994-7Online publication date: 13-Dec-2024
https://doi.org/10.1007/s11075-024-01994-7
Baker CPaul CWillé D(2023)Issues in the numerical solution of evolutionary delay differential equationsAdvances in Computational Mathematics10.1007/BF029886253:1(171-196)Online publication date: 22-Mar-2023
https://dl.acm.org/doi/10.1007/BF02988625
Farhloul MFortin M(2023)A mixed finite element for the stokes problem using quadrilateral elementsAdvances in Computational Mathematics10.1007/BF024319983:1-2(101-113)Online publication date: 22-Mar-2023
https://dl.acm.org/doi/10.1007/BF02431998
Isaia V(2021)A Fixed Point Approach to Simulation of Functional Differential Equations with a Delayed ArgumentJournal of Dynamics and Differential Equations10.1007/s10884-021-10081-735:2(1047-1082)Online publication date: 7-Oct-2021
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Baker CPaul CWillé D(1995)Issues in the numerical solution of evolutionary delay differential equationsAdvances in Computational Mathematics10.1007/BF030283703:3(171-196)Online publication date: 1-Apr-1995
https://dl.acm.org/doi/10.1007/BF03028370
Lew A(1986)Richard Bellman's contributions to computer scienceJournal of Mathematical Analysis and Applications10.1016/0022-247X(86)90146-0119:1-2(90-96)Online publication date: Oct-1986
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(1973)BibliographyIntroduction to the Theory and Application of Differential Equations with Deviating Arguments10.1016/S0076-5392(08)62979-3(293-357)Online publication date: 1973
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Feldstein AGrafton CBlue RRosenberg A(1968)Experimental mathematicsProceedings of the 1968 23rd ACM national conference10.1145/800186.810567(67-71)Online publication date: 1-Jan-1968
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(1967)14 Some Directions of ResearchIntroduction to the Mathematical Theory of Control Processes: Nonlinear Processes10.1016/S0076-5392(08)62945-8(289-297)Online publication date: 1967
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