Fictitious centre RBF method for high order BVPs in multiply connected domains

We propose a Kansa-radial basis function (RBF) collocation method for the solution of 2D and 3D high order (i.e. of order 2N where N is an element of N, N >= 3) boundary value problems (BVPs) in multiply connected domains. These problems include N boundary conditions (BCs), and thus we need to select N distinct sets of boundary centres. One set is positioned on the physical boundary of the problem while the rest are placed outside the exterior boundary of the domain. The efficacy of the proposed approach is demonstrated by applying it to a 2D and a 3D high order BVP in multiply connected domains. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

A Kansa-radial basis function collocation method is proposed for solving high order BVPs in multiply connected domains, where N distinct sets of boundary centers are selected. The efficacy of the proposed approach has been demonstrated through applications in 2D and 3D high order BVPs in multiply connected domains.