Numerical methods based on additive splittings for hyperbolic partial differential equations
Authors:
Randall J. LeVeque and Joseph Oliger
Journal:
Math. Comp. 40 (1983), 469497
MSC:
Primary 65M05
MathSciNet review:
689466
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Abstract: We derive and analyze several methods for systems of hyperbolic equations with wide ranges of signal speeds. These techniques are also useful for problems whose coefficients have large mean values about which they oscillate with small amplitude. Our methods are based on additive splittings of the operators into components that can be approximated independently on the different time scales, some of which are sometimes treated exactly. The efficiency of the splitting methods is seen to depend on the error incurred in splitting the exact solution operator. This is analyzed and a technique is discussed for reducing this error through a simple change of variables. A procedure for generating the appropriate boundary data for the intermediate solutions is also presented.
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 A. J. Gadd, "A split explicit integration scheme for numerical weather prediction," Quart. J. Roy. Met. Soc., v. 104, 1978, pp. 569582.
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 A. R. Gourlay, "Splitting methods for time dependent partial differential equations," in The State of the Art in Numerical Analysis (D. Jacobs, ed.), Academic Press, New York, 1977. MR 0451759 (56:10041)
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 B. Gustafsson, "The convergence rate for difference approximations to mixed initial boundary value problems," Math. comp., v. 29, 1975, pp. 396406. MR 0386296 (52:7154)
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 [16]
 G. Strang, "On the construction and comparison of difference schemes," SIAM J. Numer. Anal., v. 5, 1968, pp. 506517. MR 0235754 (38:4057)
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 J. Strikwerda, A TimeSplit Difference Scheme for the Compressible NavierStokes Equations With Applications to Flows in Slotted Nozzles, ICASE Report No. 8027, 1980.
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 E. Turkel & G. Zwas, "Explicit large timestep schemes for the shallow water equations," AICA Proc., No. 3, 1979, pp. 6569.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198306894668
PII:
S 00255718(1983)06894668
Article copyright:
© Copyright 1983 American Mathematical Society
