A rational approximation and its applications to differential equations on the half line. (English) Zbl 0984.65104

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.


65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
41A20 Approximation by rational functions
34B05 Linear boundary value problems for ordinary differential equations
35K05 Heat equation
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
65D05 Numerical interpolation
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