New RBF Collocation Methods and Kernel RBF with Applications

  • Wen Chen
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 26)


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.


Radial Basis Function Kernel Radial Basis Function Move Less Square Meshfree Method Radial Basis Function Interpolation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Wen Chen
    • 1
  1. 1.Department of InformaticsUniversity of OsloOsloNorway

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