Fictitious centre RBF method for high order BVPs in multiply connected domains. (March 2022)

• Record Type: Journal Article
• Authors: Karageorghis, Andreas; Noorizadegan, Amir; Chen, C.S.
• Is Part Of: Applied mathematics letters. Volume 125(2022)
• Publication Date: 2022-03
• Subjects: RBFs -- Kansa method -- High order PDEs -- Fictitious point method -- Multiquadrics -- Multiply connected domains; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2021.107711
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: We propose a Kansa-radial basis function (RBF) collocation method for the solution of 2D and 3D high order (i.e. of order 2 N where N ∈ 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.