Improved Kansa RBF method for the solution of nonlinear boundary value problems. (February 2018)

• Record Type: Journal Article
• Authors: Jankowska, Malgorzata A.; Karageorghis, Andreas; Chen, C.S.
• Is Part Of: Engineering analysis with boundary elements. Volume 87(2018)
• Page Start: 173
• Page End: 183
• Publication Date: 2018-02
• Subjects: Radial basis functions -- Kansa method -- Collocation; 65N35 -- 65H10; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2017.11.012
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: We apply the Kansa–radial basis function (RBF) collocation method to two-dimensional nonlinear boundary value problems. In it, the solution is approximated by a linear combination of RBFs and the governing equation and boundary conditions are satisfied in a collocation sense at interior and boundary points, respectively. The nonlinear system of equations resulting from the Kansa–RBF discretization for the unknown coefficients in the RBF approximation is solved by directly applying a standard nonlinear solver. In a natural way, the value of the shape parameter in the RBFs employed in the approximation may be included in the unknowns to be determined. The numerical results of several examples are presented and analyzed.