非线性问题的Kansa RBF方法

THE INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS AND EXPERIMENTAL MEASUREMENTS Pub Date : 2018-01-01 DOI:10.2495/CMEM-V6-N6-1000-1007

M. Jankowska, A. Karageorghis, Chingshyang Chen

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引用次数: 14

摘要

将Kansa-radial基函数(RBF)配置方法应用于二维非线性边值问题。直接应用标准非线性求解器求解由Kansa-RBF离散引起的非线性方程组。以一种自然的方式，在近似中使用的rbf中形状参数的值包含在待确定的未知数中。给出了一些算例的数值计算结果并进行了分析。

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Kansa RBF method for nonlinear problems

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 discretiza- tion 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.

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THE INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS AND EXPERIMENTAL MEASUREMENTS

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