Dr David Griffiths

References of Papers: History of Numerical PDEs

1. L. F. Richardson, The approximate arithmetical solution by finite differences of physical problems involving differential equations with applications to the stress in a masonry dam, Phil. Trans. Roy. Soc. London, A210, 307-357, 1910.
2. L. F. Richardson, Weather Prediction by Numerical Process, 1922, Cambridge University Press
3. L. F. Richardson & J. A. Gaunt, The deferred approach to the limit, Phil. Trans. Roy. Soc. London, Ser. A, vol. 226,229-361, 1927
4. R. Courant, K. Friedrichs & H. Lewy, Uber die partiellen Differenzengleichungen der mathematischen Physik, Math. Ann., 100,32-,1928. Translated by Phyllis Fox: On the partial differential equations of Mathematical Physics, AEC Res. & Dev. Report, NYO-7689, New York University, 1956
5. A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type, J. Crank & P. Nicolson, Proc. Camb. Phil. Soc., 43, 50-67, 1947.
6. G. G. O'Brien, M. A. Hyman & S. Kaplan, A study of the numerical solution of partial differential equations, J. Math. Physics, 29, 223-251 (1951)
7. A. R. Mitchell, Relaxation Methods in Compressible Flow, Ph D Thesis, St Andrews, (1950)
8. R. V. Southwell & D. N. de G. Allen, Relaxation methods applied to determine the motion in two dimensions of a viscous fluid past a fixed cylinder, Quart. J. Mech. Appl. Math., 129-145, 8, 1955.
9. A. M. Il'in, Differencing scheme for a differential equation with a small parameter affecting the highest derivative, Math. Notes Acad. Sci. USSR, 6, 592-602(1969)
10. D N de G Allen, Relaxation Methods in Engineering and Science, McGraw Hill, 1954.

Links Related to the History of Numerical PDEs

• Lewis Fry Richardson Home page, University of Paisley, Scotland.
• Lewis Fry Richardson From Wikipedia, the free encyclopedia
• Lewis Fry Richardson (1881-1953)- a short biography ( St Andrews University History of Mathematics archive)
• Weather, War, and Mathematics by Philip J. Davis, SIAM News, Volume 29, Number 9, November 1996. Reviews of
  1. The Forgiving Air: Understanding Environmental Change By Richard C.J. Somerville, University of California Press, Berkeley, 1996, 195 pages, $21.95
  2. The Collected Papers of Lewis Fry Richardson, Oliver M. Ashford et al., eds., Cambridge University Press, Cambridge, 1993, 2 volumes, 500 pages each, $150.00 each
  3. Prophet or Professor? The Life and Work of Lewis Fry Richardson. By Oliver M. Ashford, A. Hilger, Boston, 1985, 309 pages
• Richardson: "The first to apply mathematical techniques to weather forecasting. Initial plan required 3 months' worth of calculations to predict weather for next 24 hours. Became practical post-Turing. Pacifist. Contributed to calculus and study of diffusion (intermingling of molecules or other small particles by random thermal motion. " From Jeff Whittington's index of mathematicians and related types: logicians, philosophers, physicists, economists, and others.
• Dr. Vannevar Bush and the Differential Analyzer (1931)
• Differential Analyser made with Meccano Tim Robinson's Meccano Computing Machinery web site
• University of Manchester, National Archive for the History of Computing
• Vannevar Bush's Analog Computer -- The Differential Analyser Notes abstracted from the book Bebop BYTES Back (An Unconventional Guide to Computers) Copyright Information
• Endless Frontier: Vannevar Bush, Engineer of the American Century, G. Pascal Zachary, The Free Press, N.Y., 1997, 512 pages, $32.50. Reviewed in SIAM News, Vol 31, No. 10, Dec. 1998: Vannevar Bush: The History of his Moment, His Moment in History, Richard H. Herman.
  See also:
  Memex (a portmanteau of "memory extender") is the name given by Vannevar Bush to the theoretical proto-hypertext computer system he proposed in his 1945 The Atlantic Monthly article "As We May Think".
• Olaus Magnus Friedrich Erdmann Henrici (1840-1918) "...he introduced a Mechanics Laboratory and a Harmonic Analyser." (MacTutor History of Mathematics archive)
• Slide Rule Instructions.
• William Henry Wittrick 1922-1986, "...the method of analysis was based on Sir Richard Southwell's tension coefficient method and was set out in tabular form, whilst the arithmetic was done on a Fuller calculator, a slide rule with a scale 500 in. long in the form of a helix on a cylinder about 3 in. in diameter.
• " The history of computation at Queen's began in the early 1860s when James Thomson invented an analog integrator, known as the Differential Analyser, which was used by his brother, Lord Kelvin, for computing tide tables. The tradition of computation was continued by Sir David Bates FRS, who used a differential analyser when he was a student at Queen's in the 1930s. Later, in 1959, he established the first lectureship in Digital Computing within the Department of Applied Mathematics and purchased the university's first digital computer, a DEUCE, in 1961." From The Queen's University of Belfast, Department of Computer Science.