Meshfree explicit local radial basis function collocation method for diffusion problems

By Bozidar Sarler, Robert Vertnik. Computers and Mathematics with Applications, 2006

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Assessment of global and local meshless methods based on collocation with radial basis functions for parabolic partial differential equations in three dimensions (2012, methodology): “In recent years radial basis functions (RBFs) have been extensively used in different applications [2,3,5,17,32,36,37,39,43] and emerged as a potential alternative in the field of numerical solution of partial differential equations (PDEs).”
Stable Computations with Gaussian Radial Basis Functions (2011, methodology): “The RBF-QR method opens up new possibilities for all methods based on local RBF approximation, such as RBF domain decomposition methods [1], [20] and RBFgenerated scattered node finite differences [10], [24], [25], [27], [30], since it is now possible to compute for the best shape parameter value ev”
The Localized RBFs Collocation Methods for Solving High Dimensional PDEs (2013, neutral): “[8], Sarler and Vertnik [10], and Yao et al.”
Meshless local radial basis function collocation method for convective‐diffusive solid‐liquid phase change problems (2006, methodology): “The developments are based on our experience ( Sarler and Vertnik, 2005”