Timeline of numerical analysis after 1945

The following is a timeline of numerical analysis after 1945, and deals with developments after the invention of the modern

• 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]

• Successive over-relaxation was devised simultaneously by D.M. Young Jr.^[7] and by H. Frankel in 1950.
• National Bureau of Standards, initiate the development of Krylov subspace iteration methods.^{[8][9][10][11]}
  Voted one of the top 10 algorithms of the 20th century.
• Equations of State Calculations by Fast Computing Machines introduces the Metropolis–Hastings algorithm.^[12]
• In numerical differential equations, Lax and Friedrichs invent the Lax-Friedrichs method.[13]^[14]
• Householder invents his
  eponymous matrices and transformation method (voted one of the top 10 algorithms of the 20th century).^[15]
• Romberg integration^[16]
• QR factorization
  (voted one of the top 10 algorithms of the 20th century).

• 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
  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.