Difference Engine

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Difference Engine

(computer, history)
Charles Babbage's design for the first automatic mechanical calculator. The Difference Engine was a special purpose device intended for the production of mathematical tables. Babbage started work on the Difference Engine in 1823 with funding from the British Government. Only one-seventh of the complete engine, about 2000 parts, was built in 1832 by Babbage's engineer, Joseph Clement. This was demonstrated successfully by Babbage and still works perfectly. The engine was never completed and most of the 12,000 parts manufactured were later melted for scrap.

It was left to Georg and Edvard Schuetz to construct the first working devices to the same design which were successful in limited applications. The Difference Engine No. 2 was finally completed in 1991 at the Science Museum, London, UK and is on display there.

The engine used gears to compute cumulative sums in a series of registers: r[i] := r[i] + r[i+1]. However, the addition had the side effect of zeroing r[i+1]. Babbage overcame this by simultaneously copying r[i+1] to a temporary register during the addition and then copying it back to r[i+1] at the end of each cycle (each turn of a handle).

Difference Engine at the Science Museum.

Difference Engine

An early calculator designed by Charles Babbage and subsidized by the British government. Employing wheels and rods, which others had experimented with earlier, the project was started in 1821 but failed its test in 1833. Babbage then turned his attention to the Analytical Engine and completely abandoned the Difference Engine by 1842. Although never completed, it did improve the precision of Britain's machine-tool industry. In 1991, the National Museum of Science and Technology built a working model of the Difference Engine.

In 1879, Babbage's son reassembled a section of the Difference Engine from parts, and in 1995, Christie's auction in London auctioned off that section to the Power House Museum in Sydney for USD $282,000. The other known sections are owned by Harvard and Cambridge Universities. See Analytical Engine.

The Difference Engine
This impression from a woodcut was printed in 1853 showing a portion of the Difference Engine that was built in 1833. Babbage later turned his attention to the Analytical Engine. It, too, was never finished. (Image courtesy of Charles Babbage Institute, University of Minnesota, www.cbi.umn.edu)
References in periodicals archive ?
The theory of the method of finite differences is based on the theory of the approximation of functions, when values of them in discrete points are known.
The received formulae allowed to carry out the approximation of functions and their derivatives not resorting to differences as it is made in a classical method of grids (method of finite difference).
Abstract: The purpose of this paper is to develop and generalize the improved method of grids (method of finite differences) described in (Kollats, 1969) to calculation a partial derivative.
Generalization of the method of finite differences, Proceedings of the 21st DAAAM World Symposium, 20-23 October 2010, Zadar, ISSN 1726-9679, Katalinic, B.
The method of finite differences is widely used to solve the problems of visualization of sound propagation in the rooms and reflection from the obstacles [2, 3].
Nowadays there is tendency to use numerical methods (e.g., the method of moments [11], and the method of finite differences in time domain [12], [13]) for simulation and analysis of MMDLs.
He starts with the basic principles of electromagnetic theory, then moves to analytical methods and orthogonal functions, Green's functions, computer integration and conformal mapping, Fourier transform methods, computational methods, method of finite differences, finite difference time domain analysis, and variational methods.