Titlebook: Recent Advances in Radial Basis Function Collocation Methods; Wen Chen,Zhuo-Jia Fu,C.S. Chen Book 2014 The Author(s) 2014 Boundary Knot Me

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Radial Basis Functions,onally expensive in dealing with high dimensional problems due to their dependency on geometric complexity. Alternatively, radial basis functions (RBFs) are constructed in terms of one-dimensional distance variable irrespective of dimensionality of problems and appear to have a clear edge over the t

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Radial Basis Functions,l problem-dependent RBFs, such as fundamental solutions, general solutions, harmonic functions, and particular solutions, are presented. Based on the second Green identity, we propose the kernel RBF-creating strategy to construct the appropriate RBFs.

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Boundary-Type RBF Collocation Methods,method (MRM), the recursive composite MRM (RC-MRM), is introduced to establish a boundary-only discretization of nonhomogeneous problems. Finally, numerical demonstrations show the convergence rate and stability of these boundary-type RBF collocation methods for several benchmark examples.

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Book 2014numerical schemes for solving partial differential equations. The RBF collocation methods are inherently free of integration and mesh, and avoid tedious mesh generation involved in standard finite element and boundary element methods. This book focuses primarily on the numerical algorithms, engineer

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