History of numerical solution of differential equations using computers
Encyclopedia
According to Mary Croarken in her paper "Computing in Britain During World War II," by 1945, the Cambridge Mathematical Laboratory created by John Lennard-Jones
utilized the latest computing devices to perform the equations. These devices included a model "differential analyser
," and the Mallock machine
, described as "an electrical simultaneous equation solver." According to Croarken, the Ministry was also interested in the new arrival of a differential analyzer accommodating eight integrators. This exotic computing device built by Metropolitan-Vickers in 1939 consisted of wheel and disk mechanisms that could provide descriptions and solutions for differential equations. Output resulted in a plotted graph.
At the same time, in the United States, analog computer
pioneer Vannevar Bush took on a similar role to that of Lennard-Jones in the military effort after President Franklin Delano Roosevelt entrusted him with the bulk of wartime research into automatic control of fire power using machines and computing devices.
John Lennard-Jones
Sir John Edward Lennard-Jones KBE, FRS was a mathematician who was a professor of theoretical physics at Bristol University, and then of theoretical science at Cambridge University...
utilized the latest computing devices to perform the equations. These devices included a model "differential analyser
Differential analyser
The differential analyser is a mechanical analogue computer designed to solve differential equations by integration, using wheel-and-disc mechanisms to perform the integration...
," and the Mallock machine
Mallock machine
The Mallock machine was an electrical analog computer built in 1933 to solve simultaneous linear differential equations. It used coupled transformers, with numbers of turns digitally set up to +/-1000 and solved sets of up to 10 linear differential equations. It was built by Rawlyn Richard...
, described as "an electrical simultaneous equation solver." According to Croarken, the Ministry was also interested in the new arrival of a differential analyzer accommodating eight integrators. This exotic computing device built by Metropolitan-Vickers in 1939 consisted of wheel and disk mechanisms that could provide descriptions and solutions for differential equations. Output resulted in a plotted graph.
At the same time, in the United States, analog computer
Analog computer
An analog computer is a form of computer that uses the continuously-changeable aspects of physical phenomena such as electrical, mechanical, or hydraulic quantities to model the problem being solved...
pioneer Vannevar Bush took on a similar role to that of Lennard-Jones in the military effort after President Franklin Delano Roosevelt entrusted him with the bulk of wartime research into automatic control of fire power using machines and computing devices.
See also
- Numerical ordinary differential equationsNumerical ordinary differential equationsNumerical ordinary differential equations is the part of numerical analysis which studies the numerical solution of ordinary differential equations...
- Numerical partial differential equationsNumerical partial differential equationsNumerical partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations .Numerical techniques for solving PDEs include the following:...