High Speed Memory Analog Computer. Development of Memory Core and Solving Partial Differential Equations

1961 ◽  
Vol 53 (3) ◽  
pp. 173-180 ◽  
Author(s):  
Stanley H. Jury
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
High Speed ◽  
Analog Computer ◽  
Partial Differential ◽  
Computer Development

scholarly journals Using analog computers in today's largest computational challenges

2021 ◽  
Vol 19 ◽  
pp. 105-116
Author(s):  
Sven Köppel ◽  
Bernd Ulmann ◽  
Lars Heimann ◽  
Dirk Killat
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Energy Efficient ◽  
Large Scale ◽  
Scientific Computing ◽  
Analog Computer ◽  
Partial Differential ◽  
Technology Platform

Abstract. Analog computers can be revived as a feasible technology platform for low precision, energy efficient and fast computing. We justify this statement by measuring the performance of a modern analog computer and comparing it with that of traditional digital processors. General statements are made about the solution of ordinary and partial differential equations. Computational fluid dynamics are discussed as an example of large scale scientific computing applications. Several models are proposed which demonstrate the benefits of analog and digital-analog hybrid computing.

scholarly journals DISCRETE-TIME MODELLING OP DISPERSION IN ESTURARIES

1980 ◽  
Vol 1 (17) ◽  
pp. 182
Author(s):  
T. Wood
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
High Speed ◽  
Transport Theory ◽  
State Parameter ◽  
Space Time ◽  
Tidal River ◽  
Primary Concern ◽  
Transport Parameters ◽  
Partial Differential

This paper aims to put forward a case in favour of a simple discretetime model describing mixing in an estuary. The model derives from the remarkably simple concepts developed by Ketchum (1951 a,b) which describe mixing in terms of tidal prism exchanges between segments. The author's view is that Ketchum1s ideas were abandoned before they were fully explored. A major factor was the advent of the high-speed computer which opened up the possibility of using an approach based on the space-time formulation of the problem in terms of the partial differential equations of transport theory. Intrinsically this approach, based on a continuum description, is more attractive than a gross description based on relatively large segments: one obvious reason is the possibility of providing a comprehensive space-time prediction of the spread of a pollutant. In practice, though, significant problems arise in its use: in particular, the following can be mentioned - a) substantial computing costs relating to computer program development and machine time b) specification of transport parameters inherent in the partial differential equations of transport: for example, dispersion coefficients c) model validation and state/parameter estimation. The last of these is the primary concern of this paper. It is probably true to say that, to date, too little attention has been given to these topics, in the context of estuarine modelling. The point to be made is that there is small justification in using a sophisticated description of a system if the resulting predictions of the model cannot be effectively validated. The ideas used in this paper stem from those put forward by Beck and Young (1975) in studies on non-tidal river pollution. The subsequent discussion suggests an extension to estuarine systems-.

Dynamic Response of a High-Speed Slider-Crank Mechanism With an Elastic Connecting Rod

1975 ◽  
Vol 97 (2) ◽  
pp. 542-550 ◽  
Author(s):  
S.-C. Chu ◽  
K. C. Pan
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Dynamic Response ◽  
Ordinary Differential Equations ◽  
High Speed ◽  
Polynomial Method ◽  
Connecting Rod ◽  
Partial Differential ◽  
Weighted Residuals ◽  
Crank Mechanism

To achieve the performance of a mechanism to a higher degree of accuracy requires that the elastic deformations of a member in a mechanism under dynamic loading conditions be taken into account. Coupled nonlinear governing partial differential equations have been derived for transverse and longitudinal vibrations of an elastic connecting rod in a slider-crank mechanism operating at high speed conditions. The derived coupled governing nonlinear partial differential equations of motion were transformed into ordinary differential equations by use of the Kantorovich method and the method of weighted residuals. The resulting coupled ordinary differential equations were solved numerically by use of the piecewise polynomial method and the fourth-order Runge-Kutta method. The dynamic response of the system has been investigated on the basis of natural frequencies of the first mode free vibrations, the ratios of the length of crank to the length of connecting rod, viscous damping, and rotating speeds of crank. These parameters can be used by the designer to predict the vibrations of an elastic mechanism under high-speed conditions.

A consideration on the solution of partial differential equations by analog computer

SIMULATION ◽  
1966 ◽  
Vol 6 (2) ◽  
pp. 105-108
Author(s):  
Takeo Miura ◽  
Junzo Iwata
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Good Accuracy ◽  
Analog Computer ◽  
Optimum Number ◽  
Partial Differential ◽  
Simple Method ◽  
True Solution ◽  
Truncation Errors ◽  
Extrapolation Formula

When solving partial differential equations with an analog computer, they are usually transformed first to difference equations. This transformation causes truncation errors because of the finite number of sections. In this paper, a method is proposed whereby two solutions involving trun cation errors are extrapolated to find the true solution. The proposed extrapolation formula is based on the fact that the error in the solution is approximately proportional to the square of the section length. It is a quite simple method and has a wide area of application. Application to the diffusion equation resulted in good accuracy. The method is shown to be effective in estimating the error and the optimum number of sections in a traditional dif ference equation solution.

Improving the analog simulation of partial differential equations by hybrid computation

SIMULATION ◽  
1968 ◽  
Vol 11 (2) ◽  
pp. 73-80 ◽  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Adaptive Sampling ◽  
Analog Computer ◽  
Correction Function ◽  
Partial Differential ◽  
Analog Simulation ◽  
Error Corrections ◽  
Hybrid Computation ◽  
Truncated Fourier Series

The conventional analog computer simulation of partial differential equations is very useful, especially where fast repetitive runs are desired. However, the rough approxi mations in the space derivatives obtained by differencing one or more of the space variables in a time-independent equation can lead to considerable error. We propose here several methods of correcting this error which require hy brid computation for their meaningful use. The integrator outputs from each "cell" of the analog computer are sampled simultaneously, and these sample values are then processed numerically in the digital com puter to produce corrections to the derivative first-order approximations being mechanized on the analog com puter. These corrections are supplied to the analog solu tion through the DAC as a continuous correction function throughout the time transient. We have, so far, found that the best method of computing these corrections is based on the truncated Fourier series. We also found that axis transformations can be used very simply and effectively to compute better derivative approximations. By the transformation, samples are bunched in the more active and spread in the less active space regions in a type of adaptive sampling. The digital computer easily computes the necessary transformations and automatically sets the analog potentiometers. Using these two methods, together with some calcula tions to prevent error-noise corruption, we obtained error corrections of the order of 15 to 30 percent in some de rivative approximations now in common use.

Matrix and other direct methods for the solution of systems of linear difference equations

1960 ◽  
Vol 252 (1005) ◽  
pp. 69-131 ◽  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Difference Equations ◽  
High Speed ◽  
Direct Methods ◽  
Approximate Solutions ◽  
Small Scale ◽  
Linear Difference Equations ◽  
Partial Differential ◽  
Linear Partial Differential Equations

The investigations described in this paper were initiated in an attempt to replace by direct methods the successive approximation methods such as those of Southwell and Thom for the solution of systems of difference equations arising in the approximate solutions of linear partial differential equations. Boundary problems of this type form the subject of part III, which is the kernel of the paper. As the work progressed it was found that the methods evolved were applicable, and capable of extension, to step-by-step solutions also, and to ordinary as well as partial differential equations. These topics are presented in parts I, II and IV. Matrix methods naturally predominate. The methods are illustrated by small-scale examples worked on desk machines, but the operations involved are, we believe, capable of being handled efficiently and simply by modern high-speed digital computers.

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