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Zbl 0984.65104
Guo, Benyu; Shen, Jie; Wang, Zhongqing
A rational approximation and its applications to differential equations on the half line. (English)
[J] J. Sci. Comput. 15, No.2, 117-147 (2000). ISSN 0885-7474; ISSN 1573-7691/e

The system of orthogonal rational functions induced by the Legendre polynomials and its basic properties are introduced. Various orthogonal projections are studied and established some results on rational approximation are established. Two kinds of rational interpolation are considered. A rational spectral method and a rational pseudospectral method for two model problems are analyzed. Finally, some numerical implementations and numerical results are presented which agree well with the theoretical analysis and which demonstrate the effectiveness of the considered approach.
[F.Pérez Acosta (La Laguna)]

MSC 2000:: *65M70 Spectral, collocation and related methods (IVP of PDE)
41A20 Approximation by rational functions
34B05 Linear boundary value problems of ODE
35K05 Heat equation
65L60 Finite numerical methods for ODE
65D05 Interpolation (numerical methods)

Keywords: differential equations on the half line; orthogonal rational functions; Legendre polynomials; rational interpolation; spectral method; pseudospectral method; numerical results

Cited in: Zbl 0992.65111

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