Abstract
This chapter examines the Von Neumann test for stability. It is applicable to finite difference schemes for partial differential equations. It yields knowledge of whether the difference scheme is stable. The Von Neumann test determines if the difference scheme for a partial differential equation is stable. For difference schemes with constant coefficients, the test consists of examining all exponential solutions to determine whether they grow exponentially in the time variable even when the initial values are bounded functions of the space variable. It is found that if any of them do increase without limit then the method is unstable. This test can also be applied to equations with variable coefficients by introducing new, constant coefficients equal to the frozen values of the original ones at some specific point of interest.
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