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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Stable difference schemes with uneven mesh spacings

Author: Melvyn Ciment
Journal: Math. Comp. 25 (1971), 219-227
MSC: Primary 65N10
MathSciNet review: 0300470
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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 ${L_2}$ 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