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Convergence order estimates of meshless collocation methods using radial basis functions. (English) Zbl 0909.65088
A meshless collocation method using radial basis functions is considered. It allows to approximate regular solutions of systems of equations with differential or integral operators. The authors establish error bounds. The results are applied to the mixed linear problems. The suggested method may be considered as one of the emerging meshless methods. As an example the boundary value problem for an elliptic operator is studied.

MSC:
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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