In this paper, we propose a new Kansa method with fictitious centre approach in which the radial basis function (RBF) approximation is augmented by polynomial basis functions. The proposed approach considerably improves not only the accuracy but also the stability of the recently proposed ghost point method using radial basis functions. The difficulty of selecting a good RBF shape parameter is no longer an issue. Two numerical examples are presented to show the effectiveness and the improvement of the proposed method over previous methods.

中文翻译：

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使用RBF和多项式基函数的重影点方法

在本文中，我们提出了一种新的具有虚拟中心法的Kansa方法，其中径向基函数（RBF）逼近被多项式基函数所增强。所提出的方法不仅大大提高了最近提出的使用径向基函数的重影点方法的准确性，而且还提高了其稳定性。选择良好的RBF形状参数的困难不再是问题。给出了两个数值例子，说明了该方法的有效性和对以前方法的改进。