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Mathematics of Computation

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Stability theory of difference approximations for multidimensional initial-boundary value problems

Author: Daniel Michelson
Journal: Math. Comp. 40 (1983), 1-45
MSC: Primary 65M10
MathSciNet review: 679433
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Abstract: A stability theory is developed for dissipative difference approximations to multidimensional initial-boundary value problems. The original differential problem should be strictly hyperbolic and the difference problem consistent with the differential one. An algebra of pseudo-difference operators is built and later used to prove the stability of the difference approximation with variable coefficients. In addition, stability of the Cauchy problem for weakly dissipative difference approximations with variable coefficients is proved.

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Keywords: Stability theory, initial-boundary value problems, difference approximations, hyperbolic systems
Article copyright: © Copyright 1983 American Mathematical Society