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On the asymptotic convergence of collocation methods with spline functions of even degree. (English) Zbl 0623.65145

The authors investigate the asymptotic convergence of the collocation method using even-degree polynomial splines applied to strongly elliptic systems of pseudo-differential equations on closed curves with convolutional principal part. The method is equivalent to a version of the Petrov-Galerkin method and allows to state the Babuška stability condition. Optimal error estimates on the scale of Sobolev spaces are given.
Reviewer: G.Vainikko

MSC:

65R20 Numerical methods for integral equations
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
45K05 Integro-partial differential equations
35S15 Boundary value problems for PDEs with pseudodifferential operators
74S30 Other numerical methods in solid mechanics (MSC2010)
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