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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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