The Adaptation of the Cross Validation Aproach for RBF-Based Collocation Methods

[1] Belytschko T., Krongauz Y., Organ D., Flrming M., Krysl P., Meshless methods: an overview and recent developments, Computer Methods in Applied Mechanics and Engineering, vol. 139, 1996, 3-47.10.1016/S0045-7825(96)01078-XSearch in Google Scholar

[2] Liu G.R., Meshlees Methods – Moving beyond the Finite Element Method, CRC Press, Boca Raton, Florida 2003.10.1201/9781420040586Search in Google Scholar

[3] Kansa E., Multiquadrics – A scattered data approximation scheme with applications to computational fluid dynamics I: Surface approximations and partial derivative estimates, Computers and Mathematics with Applications, vol. 19, 1990, 127-145.10.1016/0898-1221(90)90270-TSearch in Google Scholar

[4] Kansa E., Multiquadrics – A scattered data approximation scheme with applications to computational fluid dynamics I: Solutions to parabolic, hyperbolic, and elliptic partial differential equations, Computers and Mathematics with Applications, vol. 19, 1990, 147-161.10.1016/0898-1221(90)90271-KSearch in Google Scholar

[5] Fasshauer G.E., Meshfree Approximation Methods with Matlab, World Scientific Publishing, Singapore, 2007.10.1142/6437Search in Google Scholar

[6] Cheng A.H.D., Multiquadrics and its shape parameter – a numerical investigation of error estimate, condition number and round-off error by arbitrary precision computation, Engineering analysis with boundary elements, vol. 36, 2012, 220-239.10.1016/j.enganabound.2011.07.008Search in Google Scholar

[7] Ferreira A.J.M, A formulation of the multiquadric radial basis function method for the analysis of laminated composite plates, Composit Structures, vol. 59, 2003, 385-92.10.1016/S0263-8223(02)00239-8Search in Google Scholar

[8] Schaback R., Error estimates and condition numbers for radial basis function interpolation, Advances in Computational Mathematics, vol. 3, 1995, 251-264.10.1007/BF02432002Search in Google Scholar

[9] Krowiak A., Radial basis function-based pseudospectral method for static analysis of thin plates, Engineering Analysis with Boundary Elements, vol. 71, 2016, 50-58.10.1016/j.enganabound.2016.07.002Search in Google Scholar

[10] Krowiak A., On choosing a value of shape parameter in Radial Basis Function collocation methods, Numerical Methods for Partial Differential Equations, submitted for publication.Search in Google Scholar

[11] Hon Y.C., Schaback R., On nonsymmetric collocation by radial basis functions, Appl. Math. Comput., vol. 119, 2001, 177-186.10.1016/S0096-3003(99)00255-6Search in Google Scholar

[12] Chen W., Fu Z.J., Chen C.S., Recent Advances in Radial Basis Function Collocation Methods, Springer, 2014.10.1007/978-3-642-39572-7Search in Google Scholar

[13] Rippa S., An algorithm for selecting a good value for the parameter c in radial basis function interpolation, Adv. in Comput. Math., vol. 11, 1999, 193-210.Search in Google Scholar