This paper considered the spectral meshless radial point interpolation (SMRPI) method to unravel for the nonlinear p-Laplacian equation with mixed Dirichlet and Neumann boundary conditions. Through this assessment, which includes meshless methods and collocation techniques based on radial point interpolation, we construct the shape functions, with the Kronecker delta function property, as basis functions in the framework of spectral collocation methods. Studies in this regard require one to evaluate the high-order derivatives without any kind of integration locally over the small quadrature domains. Finally, some examples are given to illustrate the low computing costs and high enough accuracy and efficiency of this method to solve a p-Laplacian equation and it would be of great help to fulfill the implementation related to the element-free Galerkin (EFG) method. Both the SMRPI and the EFG methods have been compared by similar numerical examples to show their application in strongly nonlinear problems.

中文翻译：

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非线性p- Laplacian方程的一种有效的无网格径向点配置方法。

本文考虑了用无谱光谱径向点插值（SMRPI）方法解开具有混合Dirichlet和Neumann边界条件的非线性p-Laplacian方程。通过此评估，包括基于径向点插值的无网格方法和配置技术，我们构造了具有Kronecker德尔塔函数性质的形状函数，并将其作为光谱配置方法框架中的基础函数。在这方面的研究要求人们评估高阶导数，而无需在小正交域上进行局部积分。最后，给出了一些例子来说明该方法的低计算成本以及足够高的精度和效率来求解p-Laplacian方程，这将对实现与无元素Galerkin（EFG）方法有关的实现有很大帮助。通过类似的数值示例对SMRPI和EFG方法进行了比较，以显示它们在强非线性问题中的应用。