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Mathematics of Computation

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Boundary conditions for a fourth order hyperbolic difference scheme

Author: D. M. Sloan
Journal: Math. Comp. 41 (1983), 1-11
MSC: Primary 65M10
MathSciNet review: 701620
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Abstract: Oliger [6] has used a stable time-averaged boundary condition with a fourth order leap-frog scheme for the numerical solution of hyperbolic partial differential equations. Gary [3] generalized the time-averaged boundary condition by including a scalar parameter. This paper examines the stability and accuracy of the more general boundary condition. The limit of the stability interval is found for the parameter, and it is shown that the parameter should be given a value close to this limit in order to minimize the boundary errors. Numerical experiments are described which support the theoretical predictions.

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Keywords: Hyperbolic equations, finite differences, stability of boundary approximations
Article copyright: © Copyright 1983 American Mathematical Society

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