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Concept
Von Neumann stability analysis
Summary
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. 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 Crank and Nicolson.
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 co-authored by John von Neumann.
Numerical stability
The stability of numerical schemes is closely associated with numerical error. A finite difference scheme is stable if the errors made at one time step of the calculation do not cause the errors to be magnified as the computations are continued. A neutrally stable scheme is one in which
Official source
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