期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 212, 期 1, 页码 99-123出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2005.05.030
关键词
radial basis functions; partial differential equations; finite difference method; compact; Mehrstellenverfahren; mesh-free
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. The generalization of compact FD formulas that we propose for scattered nodes and radial basis functions (RBFs) achieves the goal of still keeping the number of stencil nodes small 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. (c) 2005 Elsevier Inc. All rights reserved.
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