Fourth order difference methods for the initial boundaryvalue problem for hyperbolic equations
Author:
Joseph Oliger
Journal:
Math. Comp. 28 (1974), 1525
MSC:
Primary 65N05
MathSciNet review:
0359344
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Abstract: Centered difference approximations of fourth order in space and second order in time are applied to the mixed initial boundaryvalue problem for the hyperbolic equation . A method utilizing third order uncentered differences at the boundaries is shown to be stable and to retain an overall fourth order convergence estimate. Several computational examples illustrate the success of these methods for problems with one and two spacial dimensions. Further examples illustrate the effects of approximations of various orders of accuracy used at the boundaries.
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 T. Elvius & A. Sundström, "Computationally efficient schemes and boundary conditions for a finemesh barotropic model based on the shallowwater equations," Tellus, v. 25, 1973, pp. 132156.
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 B. Fornberg, On High Order Approximations of Hyperbolic Partial Differential Equations by a Fourier Method, Report 39, Department of Computer Sciences, Uppsala University, Uppsala, Sweden, 1972.
 [5]
 B. Gustafsson, On the Convergence Rate for Difference Approximations to Mixed Initial Boundary Value Problems, Report 33, Department of Computer Sciences, Uppsala University, Uppsala, Sweden, 1971.
 [6]
 B. Gustafsson, H.O. Kreiss & A. Sundström, "Stability theory of difference approximations for mixed initial boundary value problems. II," Math. Comp., v. 26, 1972, pp. 649686. MR 0341888 (49:6634)
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 H.O. Kreiss & J. Oliger, "Comparison of accurate methods for the integration of hyperbolic equations," Tellus, v. 24, 1972, pp. 199215. MR 0319382 (47:7926)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197403593447
PII:
S 00255718(1974)03593447
Article copyright:
© Copyright 1974 American Mathematical Society
