Stable difference schemes with uneven mesh spacings
Abstract: We consider a finite-difference approximation to the Cauchy problem for a firstorder hyperbolic partial differential equation using different mesh spacings in different portions of the domain. By reformulating our problem as a difference approximation to an initial-boundary value problem, we are able to use the theory of H. O. Kreiss and S. Osher to analyze the stability of our scheme.
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Keywords: Difference methods, stability, mixed initial-boundary value problems, mesh refinement
Article copyright: © Copyright 1971 American Mathematical Society