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Error bounds for solving pseudodifferential equations on spheres by collocation with zonal kernels. (English) Zbl 1004.65108

Author’s abstract: The problem of solving pseudodifferential equations on spheres by collocation with zonal kernels is considered and bounds for the approximation error are established. The bounds are given in terms of the maximum separation distance of the collocation points, the order of the pseudodifferential operator, and the smoothness of the employed zonal kernel. A by-product of the results is an improvement on the previously known convergence order estimates for Lagrange interpolation.

MSC:

65N15 Error bounds for boundary value problems involving PDEs
41A05 Interpolation in approximation theory
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35S15 Boundary value problems for PDEs with pseudodifferential operators
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