New RBF collocation methods and kernel RBF with applications

Details New RBF collocation methods and kernel RBF with applications New RBF collocation methods and kernel RBF with applications

2001-11-30

arxiv.org/abs/cs/0111063v1

Computer Science

Numerical Analysis

Welcom any comments to wenc@simula.no

Scientific paper

A few novel radial basis function (RBF) discretization schemes for partial differential equations are developed in this study. For boundary-type methods, we derive the indirect and direct symmetric boundary knot methods. Based on the multiple reciprocity principle, the boundary particle method is introduced for general inhomogeneous problems without using inner nodes. For domain-type schemes, by using the Green integral we develop a novel Hermite RBF scheme called the modified Kansa method, which significantly reduces calculation errors at close-to-boundary nodes. To avoid Gibbs phenomenon, we present the least square RBF collocation scheme. Finally, five types of the kernel RBF are also briefly presented.

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