Timeline of computational mathematics
1940s
- Monte Carlo simulation (voted one of the top 10 algorithms of the 20th century) invented at Los Alamos by von Neumann, Ulam and Metropolis.[1][2][3]
- First hydro simulations at Los Alamos occurred.[4][5]
- Ulam and von Neumann introduce the notion of cellular automata.[6]
1950s
- First successful weather predictions on a computer occurred.[7][8]
- Hestenes, Stiefel, and Lanczos, all from the Institute for Numerical Analysis at the National Bureau of Standards, initiate the development of Krylov subspace iteration methods.[9][10][11][12] Voted one of the top 10 algorithms of the 20th century.
- Equations of State Calculations by Fast Computing Machines introduces the Metropolis–Hastings algorithm.[13] Also, important earlier independent work by Alder and S. Frankel.[14][15]
- Fermi, Ulam and Pasta with help from Mary Tsingou, discover the Fermi-Pasta-Ulam problem.[16]
- Molecular dynamics invented by Alder and Wainwright[17]
1960s
- Molecular dynamics was invented independently by Aneesur Rahman.[18]
- Kruskal and Zabusky follow up the Fermi-Pasta-Ulam problem with further numerical experiments, and coin the term "soliton".[19][20]
- Edward Lorenz discovers the butterfly effect on a computer, attracting interest in chaos theory.[21]
- Frenchman Verlet (re)discovers a numerical integration algorithm,[22] (first used in 1791 by Delambre, by Cowell and Crommelin in 1909, and by Carl Fredrik Störmer in 1907,[23] hence the alternative names Störmer's method or the Verlet-Störmer method) for dynamics, and the Verlet list.[22]
1970s
- Mandelbrot, from studies of the Fatou, Julia and Mandelbrot sets, coined and popularized the term 'fractal' to describe these structures' self-similarity.[24][25]
- Kenneth Appel and Wolfgang Haken prove the four colour theorem, the first theorem to be proved by computer.[26][27][28]
1980s
- Fast multipole method invented by Rokhlin and Greengaard (voted one of the top 10 algorithms of the 20th century).[29][30][31]
1990s
- The appearance of the first research grids using volunteer computing - GIMPS (1996), distributed.net (1997) and Seti@Home (1999).
- Kepler conjecture is almost all but certainly proved algorithmically by Thomas Hales in 1998.
See also
- Timeline of scientific computing
- Computational mathematics
- Important publications in computational physics
References
- ^ Metropolis, N. (1987). "The Beginning of the Monte Carlo method" (PDF). Los Alamos Science. No. 15, Page 125.
{{cite journal}}:|volume=has extra text (help). Accessed 5 may 2012. - ^ S. Ulam, R. D. Richtmyer, and J. von Neumann(1947). Statistical methods in neutron diffusion. Los Alamos Scientific Laboratory report LAMS–551.
- ^ N. Metropolis and S. Ulam (1949). The Monte Carlo method. Journal of the American Statistical Association 44:335-341.
- ^ Richtmyer, R. D. (1948). Proposed Numerical Method for Calculation of Shocks. Los Alamos, NM: Los Alamos Scientific Laboratory LA-671.
- ^ A Method for the Numerical Calculation of Hydrodynamic Shocks. Von Neumann, J.; Richtmyer, R. D. Journal of Applied Physics, Vol. 21, p.232-237
- ^ Von Neumann, J., Theory of Self-Reproduiing Automata, Univ. of Illinois Press, Urbana, 1966.
- ^ Charney, J.; Fjørtoft, R.; von Neumann, J. (November 1950). "Numerical Integration of the Barotropic Vorticity Equation". Tellus 2 (4).
- ^ See the review article:- Smagorinsky, J (1983). "The Beginnings of Numerical Weather Prediction and General Circulation Modelling: Early Recollections" (PDF). Advances in Geophysics. 25. Retrieved 6 June 2012.
- ^ Magnus R. Hestenes and Eduard Stiefel, Methods of Conjugate Gradients for Solving Linear Systems, J. Res. Natl. Bur. Stand. 49, 409–436 (1952).
- ^ Eduard Stiefel,U¨ ber einige Methoden der Relaxationsrechnung (in German), Z. Angew. Math. Phys. 3, 1–33 (1952).
- ^ Cornelius Lanczos, Solution of Systems of Linear Equations by Minimized Iterations, J. Res. Natl. Bur. Stand. 49, 33–53 (1952).
- ^ Cornelius Lanczos, An Iteration Method for the Solution of the Eigenvalue Problem of Linear Differential and Integral Operators, J. Res. Natl. Bur. Stand. 45, 255–282 (1950).
- ^ Metropolis, N.; Rosenbluth, A.W.; Rosenbluth, M.N.; Teller, A.H.; Teller, E. (1953). "Equations of State Calculations by Fast Computing Machines". Journal of Chemical Physics. 21 (6): 1087–1092. Bibcode:1953JChPh..21.1087M. doi:10.1063/1.1699114.
- ^ Unfortunately, Alder's thesis advisor was unimpressed, so Alder and Frankel delayed publication of their results until much later. Alder, B. J. , Frankel, S. P. , and Lewinson, B. A. , J. Chem. Phys., 23, 3 (1955).
- ^ http://www.hp9825.com/html/stan_frankel.html
- ^ Fermi, E. (posthumously); Pasta, J.; Ulam, S. (1955) : Studies of Nonlinear Problems (accessed 25 Sep 2012). Los Alamos Laboratory Document LA-1940. Also appeared in 'Collected Works of Enrico Fermi', E. Segre ed. , University of Chicago Press, Vol.II,978–988,1965. Recovered 21 Dec 2012
- ^ Alder, B. J.; T. E. Wainwright (1959). "Studies in Molecular Dynamics. I. General Method". J. Chem. Phys. 31 (2): 459. Bibcode 1959JChPh..31..459A. doi:10.1063/1.1730376
- ^ Rahman, A (1964). "Correlations in the Motion of Atoms in Liquid Argon". Phys Rev. 136 (2A): A405 – A41. Bibcode:1964PhRv..136..405R. doi:10.1103/PhysRev.136.A405.
- ^ Zabusky, N. J.; Kruskal, M. D. (1965). "Interaction of 'solitons' in a collisionless plasma and the recurrence of initial states". Phys. Rev. Lett. 15 (6): 240–243. Bibcode 1965PhRvL..15..240Z. doi:10.1103/PhysRevLett.15.240.
- ^ http://www.merriam-webster.com/dictionary/soliton ; retrieved 3 nov 2012.
- ^ Lorenz, Edward N. (1963). "Deterministic Nonperiodic Flow" (PDF). Journal of the Atmospheric Sciences 20 (2): 130–141. 20 (2): 130. Bibcode:1963JAtS...20..130L. doi:10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2.
- ^ a b Verlet, Loup (1967). "Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard−Jones Molecules". Physical Review. 159: 98–103. Bibcode:1967PhRv..159...98V. doi:10.1103/PhysRev.159.98.
- ^ Press, WH; Teukolsky, SA; Vetterling, WT; Flannery, BP (2007). "Section 17.4. Second-Order Conservative Equations". Numerical Recipes: The Art of Scientific Computing (3rd ed.). New York: Cambridge University Press. ISBN 978-0-521-88068-8.
- ^ B. Mandelbrot; Les objets fractals, forme, hasard et dimension (in French). Publisher: Flammarion (1975), ISBN 9782082106474; English translation Fractals: Form, Chance and Dimension. Publisher: Freeman, W. H & Company. (1977). ISBN 9780716704737.
- ^ Mandelbrot, Benoît B.; (1983). The Fractal Geometry of Nature. San Francisco: W.H. Freeman. ISBN 0-7167-1186-9.
- ^ Kenneth Appel and Wolfgang Haken, "Every planar map is four colorable, Part I: Discharging," Illinois Journal of Mathematics 21: 429–490, 1977.
- ^ Appel, K. and Haken, W. "Every Planar Map is Four-Colorable, II: Reducibility." Illinois J. Math. 21, 491-567, 1977.
- ^ Appel, K. and Haken, W. "The Solution of the Four-Color Map Problem." Sci. Amer. 237, 108-121, 1977.
- ^ L. Greengard, The Rapid Evaluation of Potential Fields in Particle Systems, MIT, Cambridge, (1987).
- ^ Rokhlin, Vladimir (1985). "Rapid Solution of Integral Equations of Classic Potential Theory." J. Computational Physics Vol. 60, pp. 187-207.
- ^ L. Greengard and V. Rokhlin, "A fast algorithm for particle simulations," J. Comput. Phys., 73 (1987), no. 2, pp. 325–348.