Improved Kansa RBF Method for the Solution of Nonlinear Boundary Value Problems

Authors

Malgorzata A. Jankowska, Poznan University of TechnologyFollow
Andreas Karageorghis, University of CyprusFollow
Ching-Shyang Chen, University of Southern MississippiFollow

Document Type

Article

Publication Date

2-2018

Department

Mathematics

School

Mathematics and Natural Sciences

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.

Comments

© 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/.

Publication Title

Engineering Analysis with Boundary Elements

Volume

87

First Page

173

Last Page

183

Recommended Citation

Jankowska, M. A., Karageorghis, A., Chen, C. (2018). Improved Kansa RBF Method for the Solution of Nonlinear Boundary Value Problems. Engineering Analysis with Boundary Elements, 87, 173-183.
Available at: https://aquila.usm.edu/fac_pubs/14918