Abstract We consider the application of the Kansa–radial basis function (RBF) collocation method to two–dimensional fourth order boundary value problems (BVPs). The presence of two boundary conditions makes it necessary to use a second set of centres corresponding to the second boundary condition. One option is to take these centres on the boundary but at different positions to the original boundary centres. A second option is to place them on a curve surrounding the physical boundary of the problem under consideration. The two approaches are applied to several numerical examples and their results are compared and analyzed.

中文翻译：

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用于四阶 BVP 的带有辅助边界中心的 Kansa RBF 方法

摘要 我们考虑 Kansa-径向基函数 (RBF) 搭配方法在二维四阶边值问题 (BVP) 中的应用。两个边界条件的存在使得必须使用对应于第二个边界条件的第二组中心。一种选择是在边界上取这些中心，但在与原始边界中心不同的位置。第二种选择是将它们放置在围绕所考虑问题的物理边界的曲线上。将这两种方法应用于几个数值例子，并对它们的结果进行比较和分析。