A method of taking the delay of a digital automaton of a quasianalog hybrid computing system into account in solving ordinary differential equations

Cybernetics ◽  
1972 ◽  
Vol 5 (3) ◽  
pp. 277-280
Author(s):  
G. E. Pukhov
SIMULATION ◽  
1965 ◽  
Vol 4 (2) ◽  
pp. 104-116 ◽  
Author(s):  
Otto A. Reichardt ◽  
Merlin W. Hoyt ◽  
W. Thad Lee

TRICE hybrid computing systems are currently in volved in aerospace simulations that are interesting and sophisticated. Indeed it would seem that these applications are so successful that an increasing wave of interest can be expected in such DDA applications. Unlike earlier DDA's, the parallel digital differential analyzer, we believe, combines more of the best fea tures of analog and digital machines: It boasts speed, accuracy, and ease of programming. Because the machine itself is entirely digital, it couples naturally and inexpensively with convention al digital computers. Unlike other digital machines with central memory and sequential operation, all elements of this DDA operate simultaneously, thus providing rapid solutions to nonlinear differential equations characteristic of analog computers. And like its analog cousin, our DDA is programmed read ily via a patchboard, by connecting its computing elements in direct correspondence to the elements of differential equations. In one sense, TRICE is more properly a hybrid— a unique combination of analog and digital machine characteristics—than are the combinations of analog and digital computers currently being interfaced. Yet it can also be connected with analog and/or digital computers. Here we would like to explain how TRICE works, compare its advantages as a hybrid element, and con clude with a review of some current applications.


Author(s):  
V. F. Edneral ◽  
O. D. Timofeevskaya

Introduction:The method of resonant normal form is based on reducing a system of nonlinear ordinary differential equations to a simpler form, easier to explore. Moreover, for a number of autonomous nonlinear problems, it is possible to obtain explicit formulas which approximate numerical calculations of families of their periodic solutions. Replacing numerical calculations with their precalculated formulas leads to significant savings in computational time. Similar calculations were made earlier, but their accuracy was insufficient, and their complexity was very high.Purpose:Application of the resonant normal form method and a software package developed for these purposes to fourth-order systems in order to increase the calculation speed.Results:It has been shown that with the help of a single algorithm it is possible to study equations of high orders (4th and higher). Comparing the tabulation of the obtained formulas with the numerical solutions of the corresponding equations shows good quantitative agreement. Moreover, the speed of calculation by prepared approximating formulas is orders of magnitude greater than the numerical calculation speed. The obtained approximations can also be successfully applied to unstable solutions. For example, in the Henon — Heyles system, periodic solutions are surrounded by chaotic solutions and, when numerically integrated, the algorithms are often unstable on them.Practical relevance:The developed approach can be used in the simulation of physical and biological systems.


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