منابع مشابه
Efficient Embedded Formula for Chebyshev Collocation Methods
In this talk, we are concerned with embedded formulae of the Chebyshev collocation methods [1] developed recently. We introduce two Chebyshev collocation methods based on generalized Chebyshev interpolation polynomials [2], which are used to make an automatic integration method. We apply an elegant algorithm of generalized Chebyshev interpolation increasing the node points to make an error esti...
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In this paper, we introduce a generalized Chebyshev collocation method (GCCM) based on the generalized Chebyshev polynomials for solving stiff systems. For employing a technique of the embedded Runge-Kutta method used in explicit schemes, the property of the generalized Chebyshev polynomials is used, in which the nodes for the higher degree polynomial are overlapped with those for the lower deg...
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The stability of pseudospectral-Chebyshev methods is demonstrated for parabolic and hyperbolic problems with variable coefficients. The choice of collocation points is discussed. Numerical examples are given for the case of variable coefficient hyperbolic equations.
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This paper analyzes triangular finite elements for the preconditioning of Chebyshev collocation solutions of elliptic boundary value problems. Results are given for scalar model problems and for both Stokes and Navier-Stokes equations.
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We reveal the relationship between a Petrov–Galerkin method and a spectral collocation method at the Chebyshev points of the second kind (±1 and zeros of Uk) for the two-point boundary value problem. Derivative superconvergence points are identified as the Chebyshev points of the first kind (Zeros of Tk). Super-geometric convergent rate is established for a special class of solutions.
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 2004
ISSN: 0898-1221
DOI: 10.1016/s0898-1221(04)90053-3