# Timeline of numerical analysis after 1945

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The following is a timeline of numerical analysis after 1945, and deals with developments after the invention of the modern electronic computer, which began during Second World War. For a fuller history of the subject before this period, see timeline and history of 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]
• Crank–Nicolson method was developed by Crank and Nicolson. [4]
• Dantzig introduces the simplex method (voted one of the top 10 algorithms of the 20th century) in 1947. [5]
• Turing formulated the LU decomposition method. [6]

## 1960s

• First recorded use of the term "finite element method" by Ray Clough, [19] to describe the methods of Courant, Hrenikoff, Galerkin and Zienkiewicz, among others. See also here.
• Exponential integration by Certaine and Pope.
• In computational fluid dynamics and numerical differential equations, Lax and Wendroff invent the Lax-Wendroff method. [20]
• Fast Fourier Transform (voted one of the top 10 algorithms of the 20th century) invented by Cooley and Tukey. [21]
• First edition of Handbook of Mathematical Functions by Abramowitz and Stegun, both of the U.S.National Bureau of Standards. [22]
• Broyden does new quasi-Newton method for finding roots in 1965.
• The MacCormack method, for the numerical solution of hyperbolic partial differential equations in computational fluid dynamics, is introduced by MacCormack in 1969. [23]
• Verlet (re)discovers a numerical integration algorithm, (first used in 1791 by Delambre, by Cowell and Crommelin in 1909, and by Carl Fredrik Störmer in 1907, hence the alternative names Störmer's method or the Verlet-Störmer method) for dynamics.

## 1970s

Creation of LINPACK and associated benchmark by Dongarra et al., [24] [25] as well as BLAS.

## Related Research Articles

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The following timeline starts with the invention of the modern computer in the late interwar period.

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Beresford Neill Parlett is an English applied mathematician, specializing in numerical analysis and scientific computation.

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## References

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4. Crank, J. (John); Nicolson, P. (Phyllis) (1947). "A practical method for numerical evaluation of solutions of partial differential equations of the heat conduction type". Proc. Camb. Phil. Soc. 43 (1): 50–67. doi:10.1007/BF02127704. S2CID   16676040.
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16. 1955
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19. RW Clough, “The Finite Element Method in Plane Stress Analysis,” Proceedings of 2nd ASCE Conference on Electronic Computation, Pittsburgh, PA, Sept. 8, 9, 1960.
20. P.D Lax; B. Wendroff (1960). "Systems of conservation laws". Commun. Pure Appl. Math. 13 (2): 217–237. doi:10.1002/cpa.3160130205. Archived from the original on 25 September 2017.
21. Cooley, James W.; Tukey, John W. (1965). "An algorithm for the machine calculation of complex Fourier series" (PDF). Math. Comput. 19 (90): 297–301. doi:.
22. M Abramowitz and I Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Publisher: Dover Publications. Publication date: 1964; ISBN   0-486-61272-4;OCLC Number:18003605 .
23. MacCormack, R. W., The Effect of viscosity in hypervelocity impact cratering, AIAA Paper, 69-354 (1969).
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