Particular solutions of Laplacian, Helmholtz-type, and polyharmonic operators involving higher order radial basis functions

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Regularized meshless method for multiply-connected-domain Laplace problems (2006, methodology): “By employing the RBF technique [3,25], the representation of the solution for multiply-connected problem as shown in Fig.”
The Method of Approximate Particular Solutions for Solving Elliptic Problems with Variable Coefficients (2011, background): “Despite the recent advancement in obtaining the close-form particular solutions for various types of differential operators [4, 8, 13], we are still restricted to solve the linear partial differential equations.”
Kernel techniques: From machine learning to meshless methods (2006, background): “The literature contains many such pairs, and we can only cite a selection: Chen and Rashed (1998), Chen, Muleshkov and Golberg (1999b), Cheng (2000), Ramachandran and Balakrishnan (2000) and Golberg, Muleshkov, Chen and Cheng (2003).”
Recent Advances in Radial Basis Function Collocation Methods (2013, methodology): “Muleshkov et al. [33] and Cheng [34] further derived the particular solutions by Polyharmonic splines.”