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Acadlore takes over the publication of IJCMEM from 2025 Vol. 13, No. 3. The preceding volumes were published under a CC BY 4.0 license by the previous owner, and displayed here as agreed between Acadlore and the previous owner. ✯ : This issue/volume is not published by Acadlore.

Open Access
Research article

Kansa RBF Method for Nonlinear Problems

m. a. jankowska1,
a. karageorghis2,
c. s. chen3
1
Institute of Applied Mechanics, Poznan University of Technology, Poznan, Poland
2
Department of Mathematics and Statistics, University of Cyprus, Nicosia, Cyprus
3
Department of Mathematics, University of Southern Mississippi, Hattiesburg, USA
International Journal of Computational Methods and Experimental Measurements
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Volume 6, Issue 6, 2018
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Pages 1000-1007
Received: N/A,
Revised: N/A,
Accepted: N/A,
Available online: N/A
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Abstract:

We apply the Kansa–radial basis function (RBF) collocation method to two– dimensional nonlinear boundary value problems. The system of nonlinear equations resulting from the Kansa–RBF discretization 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 is included in the unknowns to be determined. The numerical results of some examples are presented and analysed.

Keywords: collocation, Kansa method, radial basis functions
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Jankowska, M. A., Karageorghis, A., & Chen, C. S. (2018). Kansa RBF Method for Nonlinear Problems. Int. J. Comput. Methods Exp. Meas., 6(6), 1000-1007. https://doi.org/10.2495/CMEM-V6-N6-1000-1007
M. A. Jankowska, A. Karageorghis, and C. S. Chen, "Kansa RBF Method for Nonlinear Problems," Int. J. Comput. Methods Exp. Meas., vol. 6, no. 6, pp. 1000-1007, 2018. https://doi.org/10.2495/CMEM-V6-N6-1000-1007
@research-article{Jankowska2018KansaRM,
title={Kansa RBF Method for Nonlinear Problems},
author={M. A. Jankowska and A. Karageorghis and C. S. Chen},
journal={International Journal of Computational Methods and Experimental Measurements},
year={2018},
page={1000-1007},
doi={https://doi.org/10.2495/CMEM-V6-N6-1000-1007}
}
M. A. Jankowska, et al. "Kansa RBF Method for Nonlinear Problems." International Journal of Computational Methods and Experimental Measurements, v 6, pp 1000-1007. doi: https://doi.org/10.2495/CMEM-V6-N6-1000-1007
M. A. Jankowska, A. Karageorghis and C. S. Chen. "Kansa RBF Method for Nonlinear Problems." International Journal of Computational Methods and Experimental Measurements, 6, (2018): 1000-1007. doi: https://doi.org/10.2495/CMEM-V6-N6-1000-1007
Jankowska M. A.， Karageorghis A.， Chen C. S.. Kansa RBF Method for Nonlinear Problems[J]. International Journal of Computational Methods and Experimental Measurements， 2018， 6(6)： 1000-1007. https://doi.org/10.2495/CMEM-V6-N6-1000-1007