A Study of the Applications of Analog Computers

Kodali, V. P.

doi:10.1109/tieci.1967.229550

Cited by 6 publications

(4 citation statements)

References 3 publications

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“…It is important to note that, in order to solve a differential equation with an analog computer, it is not necessary to know the voltage waveform at any point of the electrical network, provided that the circuit was properly constructed, the desired solution is obtained by measuring the voltage signal at the output of the circuit. We remark that analog computers are best suited for solving systems of ordinary differential equations, and aditionally, it is possible to use them to solve partial differential equations by making use of finite differences approximations 7 . Since analog computers are better suited to solve time-dependent problems, the non-temporal variable is discretized to obtain a system of nonlinear ordinary differential equations for the time variable.…”

Section: Electric Analog Computermentioning

confidence: 99%

“…An electrical analog computer is an active network composed of electrical elements, namely, resistors, capacitors and operational amplifiers which, connected together, are capable of simulating any set of linear ordinary differential equations 7 . In this case, the solutions of these equations are encoded into the time evolution of the voltage waveform produced by the analog computer.…”

Section: Introductionmentioning

confidence: 99%

“…Indeed, electrical analog devices can only work with a single independent variable when codified in time 8,9 . Nonetheless, by making use of finite-difference methods, it is also possible to solve partial differential equations 7,10 .…”

Section: Introductionmentioning

confidence: 99%

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Analog simulator of integro-differential equations with classical memristors

Barrios

Retamal

Solano

2019

Sci Rep

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An analog computer makes use of continuously changeable quantities of a system, such as its electrical, mechanical, or hydraulic properties, to solve a given problem. While these devices are usually computationally more powerful than their digital counterparts, they suffer from analog noise which does not allow for error control. We will focus on analog computers based on active electrical networks comprised of resistors, capacitors, and operational amplifiers which are capable of simulating any linear ordinary differential equation. However, the class of nonlinear dynamics they can solve is limited. In this work, by adding memristors to the electrical network, we show that the analog computer can simulate a large variety of linear and nonlinear integro-differential equations by carefully choosing the conductance and the dynamics of the memristor state variable. We study the performance of these analog computers by simulating integro-differential models related to fluid dynamics, nonlinear Volterra equations for population growth, and quantum models describing non-Markovian memory effects, among others. Finally, we perform stability tests by considering imperfect analog components, obtaining robust solutions with up to 13% relative error for relevant timescales.

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Section: Electric Analog Computermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Analog simulator of integro-differential equations with classical memristors

Barrios

Retamal

Solano

2019

Sci Rep

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“…Since an AC attempts to map a problem onto physical quantities, it is necessary to establish the mathematical relation between the problem's variables and their physical representations. This is accomplished through the use of scaling factors, in both amplitude and time [7], [9], [10]. Amplitude scaling (also known as magnitude scaling) relates a system variable to its internal representation in the computer.…”

Section: Scalingmentioning

confidence: 99%

CMOS Analog Simulators of Dynamical Systems

Araújo,

Oliveira,

Guerreiro

et al. 2024

IEEE Access

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Analog computing is based upon using physical processes to solve formal mathematical problems. In the past, it was the predominant instrument of scientific calculations. Now, as the physical limits imposed on digital devices compel research into alternate computing paradigms, a reexamination of the potentialities of analog computing is warranted. This work studies the application of analog CMOS cells toward the simulation of dynamical systems, and, more generally, solving sets of coupled time-dependent ordinary differential equations. Following a brief review of the fundamentals of systems theory and analog computing, the main set of computing elements is introduced, each comprising analog cells designed in a 130 nm process. These are subsequently applied to the realization of practical, special-purpose analog computing modules. Illustrative systems from various fields are selected for simulation. Though by no means comprehensive, these case studies highlight the capabilities of contemporary analog computing, especially in solving nonlinear problems. Circuit simulations show good agreement with solutions obtained from highorder numerical methods, at least over a limited range of system parameters. The article concludes with a brief discussion of broader analog computing applications, offering future prospects toward further exploration of its potentialities and limitations in a wide range of domains.INDEX TERMS Analog computers, differential equations, dynamical systems, integrated circuits.

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Literaturverzeichnis

Röpke¹,

Riemann²

1969

Analogcomputer in Chemie Und Biologie

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A Study of the Applications of Analog Computers

Cited by 6 publications

References 3 publications

Analog simulator of integro-differential equations with classical memristors

Analog simulator of integro-differential equations with classical memristors

CMOS Analog Simulators of Dynamical Systems

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