The Chebyshev–Legendre Method: Implementing Legendre Methods on Chebyshev Points | Zendy

Wai Sun Don | Zendy; David Gottlieb | Zendy

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The Chebyshev–Legendre Method: Implementing Legendre Methods on Chebyshev Points

Author(s) -

Wai Sun Don,

David Gottlieb

Publication year - 1994

Publication title -

siam journal on numerical analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.78

H-Index - 134

eISSN - 1095-7170

pISSN - 0036-1429

DOI - 10.1137/0731079

Subject(s) - legendre polynomials , mathematics , chebyshev pseudospectral method , chebyshev iteration , chebyshev filter , chebyshev equation , chebyshev nodes , collocation method , collocation (remote sensing) , orthogonal collocation , legendre's equation , chebyshev polynomials , associated legendre polynomials , legendre wavelet , mathematical analysis , legendre function , boundary value problem , partial differential equation , differential equation , classical orthogonal polynomials , gegenbauer polynomials , ordinary differential equation , orthogonal polynomials , computer science , discrete wavelet transform , wavelet transform , machine learning , artificial intelligence , wavelet

A new collocation method for the numerical solution of partial differential equations is presented. This method uses the Chebyshev collocation points, but, because of the way the boundary conditions are implemented, it has all the advantages of the Legendre methods. In particular $L_2 $ estimates can be easily obtained for hyperbolic and parabolic problems.

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