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High‐resolution monotone schemes based on quasi‐characteristics technique
Author(s) -
Kwak Do Young,
Levin Mikhail P.
Publication year - 2001
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.5
Subject(s) - monotone polygon , godunov's scheme , mathematics , classification of discontinuities , resolution (logic) , scheme (mathematics) , order of accuracy , partial derivative , order (exchange) , partial differential equation , numerical analysis , mathematical analysis , method of characteristics , geometry , computer science , finance , artificial intelligence , economics
In this article, we consider a new technique that allows us to overcome the well‐known restriction of Godunov's theorem. According to Godunov's theorem, a second‐order explicit monotone scheme does not exist. The techniques in the construction of high‐resolution schemes with monotone properties near the discontinuities of the solution lie in choosing of one of two high‐resolution numerical solutions computed on different stencils. The criterion for choosing the final solution is proposed. Results of numerical tests that compare with the exact solution and with the numerical solution obtained by the first‐order monotone scheme are presented. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 262–276, 2001

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