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SCATTERED NODE COMPACT FINITE DIFFERENCE-TYPE FORMULAS GENERATED FROM RADIAL BASIS FUNCTIONS

  • Grady Wright
  • Bengt Fornberg

Abstract

In standard equispaced finite difference (FD) formulas, symmetries can make the order of accuracy relatively high compared to the number of nodes in the FD stencil. With scattered nodes, such symmetries are no longer available. Thus, the number of nodes in the stencils can be relatively large compared to the resulting accuracy. The generalization of compact FD (CFD) formulas that we propose for scattered nodes and radial basis functions (RBFs) achieves the goal of reducing the number of stencil nodes without a similar reduction in accuracy. We analyze the accuracy of these new compact RBF–FD formulas by applying them to some model problems, and study the effects of the shape parameter that arises in, for example, the multi-quadric radial function.

Keywords

Finite Difference Radial Basis Function Radial Basis Function Interpolation Scattered Node Finite Difference Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer 2006

Authors and Affiliations

  • Grady Wright
    • 1
  • Bengt Fornberg
    • 2
  1. 1.Department of MathematicsUniversity of UtahUSA
  2. 2.Department of Applied MathematicsUniversity of ColoradoUSA

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