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Kansa radial basis function method with fictitious centres for solving nonlinear boundary value problems
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DOI：10.1016/j.enganabound.2020.08.001.png)
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Abstract
En 中文
A Kansa-radial basis function (RBF) collocation method is applied to two-dimensional second and fourth order nonlinear boundary value problems. The solution is approximated by a linear combination of RBFs, each of which is associated with a centre and a different shape parameter. As well as the RBF coefficients in the approximation, these shape parameter values are taken to be among the unknowns. In addition, the centres are distributed within a larger domain containing the physical domain of the problem. The size of this larger domain is controlled by a dilation parameter which is also included in the unknowns. In fourth order problems where two boundary conditions are imposed, two sets of (different) boundary centres are selected. The Kansa-RBF discretization yields a system of nonlinear equations which is solved by standard software. The proposed technique is applied to four problems and the numerical results are analyzed and discussed.
Keywords:
Radial basis functions
Kansa method
Collocation
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