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Mathematics of Computation

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



Dissipative two-four methods for time-dependent problems

Authors: David Gottlieb and Eli Turkel
Journal: Math. Comp. 30 (1976), 703-723
MSC: Primary 65M05
MathSciNet review: 0443362
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Abstract: A generalization of the Lax-Wendroff method is presented. This generalization bears the same relationship to the two-step Richtmyer method as the Kreiss-Oliger scheme does to the leapfrog method. Variants based on the MacCormack method are considered as well as extensions to parabolic problems. Extensions to two dimensions are analyzed, and a proof is presented for the stability of a Thommen-type algorithm. Numerical results show that the phase error is considerably reduced from that of second-order methods and is similar to that of the Kreiss-Oliger method. Furthermore, the (2, 4) dissipative scheme can handle shocks without the necessity for an artificial viscosity.

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Article copyright: © Copyright 1976 American Mathematical Society