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Continuous families of Lax‐Wendroff schemes
Author(s) -
Cushman John H.
Publication year - 1981
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620170704
Subject(s) - inviscid flow , mathematics , stability (learning theory) , nonlinear system , mathematical analysis , galerkin method , function (biology) , space (punctuation) , shallow water equations , computer science , classical mechanics , physics , quantum mechanics , machine learning , evolutionary biology , biology , operating system
Families of difference schemes are developed for both the linear and nonlinear inviscid Burger's equation and a system of shallow water equations. Single‐step and two‐step (Lax–Wendroff type) families are described and comparisons are made with other difference schemes. The schemes are developed using a very limited portion of a space–time continua, coupled with Galerkin's method applied over a few triangular elements. The elements are geometrically flexible as a function of a geometry factor α, creating the idea of difference families. Stability is commented on, including the continuous relationship between stability and the families of schemes as a function of α. Numerical results are presented and commented on for the system of shallow water equations and the inviscid Burger's equation. Several areas for future research are described.