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Encyclopedia > Neumann problem

In mathematics, a Neumann boundary condition imposed on an ordinary differential equation or a partial differential equation specifies the values the derivative of a solution is to take on the boundary of the domain.


In the case of an ordinary differential equation such as

on the interval [0,1] the Neumann boundary conditions take the form

y'(0) = 1
y'(1) = 2

For a partial differential equation on a domain : such as

Δy + y = 0

(Δ denotes the laplacian), the Neumann boundary condition typically takes the form

Here the vector-valued function f is specified.


  Results from FactBites:
 
John von Neumann - Wikipedia, the free encyclopedia (3939 words)
Von Neumann was invited to Princeton, New Jersey in 1930, and was one of four people selected for the first faculty of the Institute for Advanced Study (two of which were Albert Einstein and Kurt Gödel), where he was a mathematics professor from its formation in 1933 until his death.
Von Neumann was diagnosed with bone cancer or pancreatic cancer in 1957, possibly caused by exposure to radioactivity while observing A-bomb tests in the Pacific, and possibly in later work on nuclear weapons at Los Alamos, New Mexico.
Von Neumann had collaborated with the spy Klaus Fuchs on hydrogen bomb development, and the two filed a secret patent on "Improvement in Methods and Means for Utilizing Nuclear Energy" in 1946, which outlined a scheme for using an exploding fission bomb to compress fusion fuel before attempting to initiate a thermonuclear reaction.
Ben Neumann: Views From The Trenches: September 2005 Archives (9185 words)
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