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An implicit fourth order difference method for viscous flows

Authors: Daniel S. Watanabe and J. Richard Flood
Journal: Math. Comp. 28 (1974), 27-32
MSC: Primary 65N05
MathSciNet review: 0341892
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Abstract: A new implicit finite-difference scheme for viscous flows is presented. The scheme is based on Simpson's rule and two-point 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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Keywords: Partial differential equations, initial-value problems, finite-difference schemes, unconditional stability, high order accuracy, viscous flows
Article copyright: © Copyright 1974 American Mathematical Society