Arnold, Douglas N.; Wendland, Wolfgang L. On the asymptotic convergence of collocation methods. (English) Zbl 0541.65075 Math. Comput. 41, 349-381 (1983). 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 Cited in 2 ReviewsCited in 69 Documents 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 Keywords:quasioptimal order estimates; linear strongly elliptic pseudodifferential equations; method of nodal collocation; odd degree polynomial splines; boundary element methods; Galerkin method; rates of convergence PDF BibTeX XML Cite \textit{D. N. Arnold} and \textit{W. L. Wendland}, Math. Comput. 41, 349--381 (1983; Zbl 0541.65075) Full Text: DOI