×

zbMATH — the first resource for mathematics

On the asymptotic convergence of collocation methods. (English) Zbl 0541.65075
In 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.
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
PDF BibTeX XML Cite
Full Text: DOI