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.

Kansa-径向基函数（RBF）配置方法应用于二维二阶和四阶非线性边值问题。该解决方案通过RBF的线性组合来近似，每个RBF都与一个中心和一个不同的形状参数关联。以及近似的RBF系数，这些形状参数值也被视为未知数。此外，中心分布在包含问题的物理域的较大域内。这个较大域的大小由膨胀参数控制，该参数也包含在未知数中。在强加两个边界条件的四阶问题中，选择了两组（不同的）边界中心。Kansa–RBF离散化产生了一个非线性方程组，可以通过标准软件来求解。