On the asymptotic convergence of collocation methods.

*(English)*Zbl 0541.65075In this paper an interesting and well documented proof of convergence for a class of boundary element methods is presented. The analysis is restricted to one independent variable problems, including nodal collocation by odd degree polynomial splines, and is applied to systems of strongly elliptic pseudodifferential equations (including two-point boundary value problems for ordinary differential equations).

The error analysis is based on an equivalence between collocation and certain non-standard Galerkin methods and provides means of comparing collocation with the standard Galerkin approach from the point of view of numerical efficiency.

The error analysis is based on an equivalence between collocation and certain non-standard Galerkin methods and provides means of comparing collocation with the standard Galerkin approach from the point of view of numerical efficiency.

Reviewer: J.C.F.Telles

##### MSC:

65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |

65R20 | Numerical methods for integral equations |

65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |

65L60 | Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations |

35S15 | Boundary value problems for PDEs with pseudodifferential operators |

34B05 | Linear boundary value problems for ordinary differential equations |

45B05 | Fredholm integral equations |

45E05 | Integral equations with kernels of Cauchy type |

45J05 | Integro-ordinary differential equations |

65N15 | Error bounds for boundary value problems involving PDEs |

65L10 | Numerical solution of boundary value problems involving ordinary differential equations |