Scattered Node Mehrstellenverfahren-Type Formulas Generated From Radial Basis Functions

Grady B. Wright, Bengt Fornberg

Research output: Chapter in Book/Report/Conference proceedingChapter

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 mehrstellenverfahren (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 multiquadric radial function.
Original languageAmerican English
Title of host publicationComputational Methods
StatePublished - 2006

EGS Disciplines

  • Mathematics

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