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**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.

Reviewer: F.Pérez Acosta (La Laguna)

### MSC:

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 |