In recent years radial basis function collocation has become a useful alternative to finite difference and finite element methods for solving elliptic partial differential equations. RBF collocation methods have been shown numerically (see for example ) and theoretically (see [14, 13]) to be very accurate even for a small number of collocation points. In application finite difference methods often have a low approximation order and consequently can require a large grid and considerable computation to obtain a sufficiently accurate solution. RBF collocation has been applied to linear elliptic PDEs in R ² and R ³ , to time dependent problems [15, 16], and to non-linear problems .
Subjectsradial basis functions
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