Roberts, JL, A method for calculating meshless finite difference weights, International Journal for Numerical Methods in Engineering, 74, (2) pp. 321-336. ISSN 0029-5981 (2008) [Refereed Article]
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An exact method for calculating the finite difference weights for arbitrary distributed points in multiple dimensions is presented. The method avoids the numerical ill conditioning associated with a small-scale factor () by delaying the limiting of 0. The Gaussian Radial Basis function is approximated by a Taylor's series expansion in the variable , and the resultant matrix equation is solved using the Fraction Free LU decomposition method.
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