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Large stiff systems solved by Chebyshev methods
Author(s) -
Abdulle A.
Publication year - 2002
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/1617-7061(200203)1:1<508::aid-pamm508>3.0.co;2-3
Subject(s) - chebyshev filter , generalization , runge–kutta methods , mathematics , type (biology) , stability (learning theory) , chebyshev equation , chebyshev polynomials , mathematical analysis , calculus (dental) , computer science , numerical analysis , geology , medicine , classical orthogonal polynomials , dentistry , orthogonal polynomials , paleontology , machine learning
Chebyshev methods (also called stabilized methods) are explicit Runge‐Kutta methods with extended stability domains along the negative real axis. These methods are intended for large mildly stiff problems, originating mainly from parabolic PDEs. We present here new Chebyshev methods of second and fourth order called ROCK, which can be seen as a combination and a generalization of van der Houwen‐Sommeijer‐type methods and Lebedev‐type methods.