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The convergence of spline collocation for strongly elliptic equations on curves. (English) Zbl 0592.65077
This paper presents a unified asymptotic error analysis for even as well as for odd degree splines subordinate. Uniform or smoothly graded meshes are in consideration only. The asymptotic convergence of optimal order is proved.
The crucial assumption for the generalized boundary integral and integro- differential operators is strong ellipticity. The analysis is based on Fourier expansion, it extends known results to variable coefficient equations. This paper contains the first convergence proof of midpoint collocation with piecewise constant functions.
Reviewer: V.Drápalík

##### 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 35J25 Boundary value problems for second-order elliptic equations 34B05 Linear boundary value problems for ordinary differential equations 65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
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##### References:
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