An implicit fourth order difference method for viscous flows
Authors:
Daniel S. Watanabe and J. Richard Flood
Journal:
Math. Comp. 28 (1974), 2732
MSC:
Primary 65N05
MathSciNet review:
0341892
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Abstract: A new implicit finitedifference scheme for viscous flows is presented. The scheme is based on Simpson's rule and twopoint Hermite interpolation, is uniformly accurate to fourth order in time and space, and is unconditionally stable according to a Fourier stability analysis. Numerical solutions of Burger's equation are presented to illustrate the order and accuracy of the scheme.
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 C. G. Broyden, "A new method of solving nonlinear simultaneous equations," Comput. J., v. 12, 1969/70, pp. 9499. MR 39 #6509. MR 0245197 (39:6509)
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 S. Z. Burstein & A. A. Mirin, "Third order difference methods for hyperbolic equations," J. Computational Phys., v. 5, 1970, pp. 547571. MR 43 #8255. MR 0282545 (43:8255)
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 R. W. MacCormack, "Numerical solution of the interaction of a shock wave with a laminar boundary layer," Lecture Notes in Physics, v. 8, SpringerVerlag, Berlin, 1971, pp. 151163.
 [4]
 E. L. Rubin & S. Z. Burstein, "Difference methods for the inviscid and viscous equations of a compressible gas," J. Computational Phys., v. 2, 1967, pp. 178196.
 [5]
 V. V. Rusanov, "On difference schemes of third order accuracy for nonlinear hyperbolic systems," J. Computational Phys., v. 5, 1970, pp. 507516. MR 43 #1452. MR 0275699 (43:1452)
 [6]
 G. Zwas & S. Abarbanel, "Third and fourth order accurate schemes for hyperbolic equations of conservation law form," Math. Comp., v. 25, 1971, pp. 229236. MR 0303766 (46:2902)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197403418927
PII:
S 00255718(1974)03418927
Keywords:
Partial differential equations,
initialvalue problems,
finitedifference schemes,
unconditional stability,
high order accuracy,
viscous flows
Article copyright:
© Copyright 1974
American Mathematical Society
