In numerical analysis, von Neumann stability analysis (also known as Fourier stability analysis) is a procedure used to check the stability of finite difference schemes as applied to linear partial differential equations.[1] The analysis is based on the Fourier decomposition of numerical error and was developed at Los Alamos National Laboratory after having been briefly described in a 1947 article by British researchers John Crank and Phyllis Nicolson.[2]
This method is an example of explicit time integration where the function that defines governing equation is evaluated at the current time.
Later, the method was given a more rigorous treatment in an article[3] co-authored by John von Neumann.
^Analysis of Numerical Methods by E. Isaacson, H. B. Keller
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Crank, J.; Nicolson, P. (1947), "A Practical Method for Numerical Evaluation of Solutions of Partial Differential Equations of Heat Conduction Type", Proc. Camb. Phil. Soc., 43: 50–67, doi:10.1007/BF02127704
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Charney, J. G.; Fjørtoft, R.; von Neumann, J. (1950), "Numerical Integration of the Barotropic Vorticity Equation", Tellus, 2: 237–254, doi:10.3402/tellusa.v2i4.8607
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In numerical analysis, vonNeumannstabilityanalysis (also known as Fourier stabilityanalysis) is a procedure used to check the stability of finite difference...
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u_{i+1}^{n}-2u_{i}^{n}+u_{i-1}^{n}\right)} As derived using vonNeumannstabilityanalysis, the FTCS method for the one-dimensional heat equation is numerically...
John vonNeumann (/vɒn ˈnɔɪmən/ von NOY-mən; Hungarian: Neumann János Lajos [ˈnɒjmɒn ˈjaːnoʃ ˈlɒjoʃ]; December 28, 1903 – February 8, 1957) was a Hungarian...
stable Courant–Friedrichs–Lewy condition — stability condition for hyperbolic PDEs VonNeumannstabilityanalysis — all Fourier components of the error should...
the type of discretization that is used. Numerical diffusion VonNeumannstabilityanalysis numerical dispersion. Glossary of the American Meteorological...
the study of the Mössbauer effect, on which she collaborated with John vonNeumann and Harry Lipkin. Bruria Kaufman was born in New York City to a Jewish...
Foundations of Economic Analysis". American Economic Review. 38 (5): 905–910. ISSN 0002-8282. JSTOR 1811704. Neumann, J. von (1937). "Über ein ökonomisches...
numerical analysis are often linked to a 1947 paper by John vonNeumann and Herman Goldstine, but others consider modern numerical analysis to go back...
equilibria in two-person zero-sum game and its proof by John vonNeumann. VonNeumann's original proof used the Brouwer fixed-point theorem on continuous...
important contributors to the development of game theory since the work of vonNeumann and Morgenstern. With Alvin E. Roth, Shapley won the 2012 Nobel Memorial...
graduate course at KTH. First and second Dahlquist barriers SIAM 1988 John vonNeumann lecturer. SIAM 1991 Peter Henrici Prize. SIAM Germund Dahlquist Prize...
George Pólya Prize for Mathematical Exposition in 2017 and the John vonNeumann Prize in 2020 by SIAM. Trefethen has one son and one daughter from his...
Data analysis is the process of inspecting, cleansing, transforming, and modeling data with the goal of discovering useful information, informing conclusions...
imputations. The stable set of a game (also known as the vonNeumann-Morgenstern solution (vonNeumann & Morgenstern 1944)) was the first solution proposed...
problem, formulated by Alain Connes in the 1970s, is a major problem in vonNeumann algebra theory. During that time, the problem was reformulated in several...
ideas about specific types of modelling. The following was said by John vonNeumann. ... the sciences do not try to explain, they hardly even try to interpret...
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