Efficient Spectral-Galerkin Method II. Direct Solvers of Second- and Fourth-Order Equations Using Chebyshev Polynomials | Zendy

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Efficient Spectral-Galerkin Method II. Direct Solvers of Second- and Fourth-Order Equations Using Chebyshev Polynomials

Author(s) -

Jie Shen

Publication year - 1995

Publication title -

siam journal on scientific computing

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.674

H-Index - 147

eISSN - 1095-7197

pISSN - 1064-8275

DOI - 10.1137/0916006

Subject(s) - chebyshev polynomials , mathematics , galerkin method , chebyshev filter , chebyshev nodes , spectral method , chebyshev equation , chebyshev iteration , chebyshev pseudospectral method , discontinuous galerkin method , order (exchange) , mathematical analysis , classical orthogonal polynomials , finite element method , orthogonal polynomials , physics , thermodynamics , finance , economics

Efficient direct solvers based on the Chebyshev–Galerkin methods for second- and fourth-order equations are presented. They are based on appropriate base functions for the Galerkin formulation that lead to discrete systems with special structured matrices that can be efficiently inverted. Numerical results indicate that the direct solvers presented in this paper are significantly more accurate and efficient than those based on the Chebyshev-tau method.

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