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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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A note on the numerical solution of the wave equation with piecewise smooth coefficients
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by David L. Brown PDF
Math. Comp. 42 (1984), 369-391 Request permission


The numerical solution of the initial value problem for the wave equation is considered for the case when the equation coefficients are piecewise smooth. This problem models linear wave propagation in a medium in which the properties of the medium change discontinuously at interfaces. Convergent difference approximations can be found that do not require the explicit specification of the boundary conditions at interfaces in the medium and hence are simple to program. Although such difference approximations typically can only be expected to be first-order accurate, the numerical phase velocity has the same accuracy as the difference approximation would if the coefficients in the differential equation were smoooth. This is proved for the one-dimensional case and demonstrated numerically for an example in two space dimensions in which the interface is not aligned with the computational mesh.
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Math. Comp. 42 (1984), 369-391
  • MSC: Primary 65M10
  • DOI:
  • MathSciNet review: 736442