zbMATH — the first resource for mathematics

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

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)
Full Text: DOI EuDML