## On condition number of meshless collocation method using radial basis functions.(English)Zbl 1090.65132

The following linear elliptic problem $$\mathcal L u=f$$ in $$\Omega$$, $$\mathcal B u=g$$ on $$\partial\Omega$$, where $$\Omega$$ is a $$d$$-dimensional domain, with a smooth boundary $$\partial\Omega$$, whose outer unit normal direction is denoted by $$\mathbf n$$, $$f$$ is a given function of $$L^2(\Omega)$$, $$\mathcal L=\sum_{i,j}\partial_i(a_{i,j}\partial_j)+ \sum_i b_i\partial_i + C_0,\quad \mathcal B=\text{Id}$$, or $${\partial\over \partial n_L}+ \text{Id}$$, is considered. The authors give an estimate for the condition number of meshless collocation method using radial basis functions.

### MSC:

 65N35 Spectral, collocation and related methods for boundary value problems involving PDEs 65F35 Numerical computation of matrix norms, conditioning, scaling 35J25 Boundary value problems for second-order elliptic equations
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