In this paper, a localized radial basis function (RBF) method is applied to obtain a global approximation of the solution of two dimensional Klein-Gordon equation on a given bounded domain. We use the RBF partition of unity (RBF-PU) method which is based on partitioning the original domain to several patches and using the RBF approximation on each local domain. Low computational cost and well conditioned final linear system are the main advantages of this method comparing with the original (global) RBF techniques. Numerical experiments show that the given problem could be solved successfully with a reasonable accuracy.

中文翻译：

---

求解 Klein-Gordon 方程的统一方法的 RBF 划分

在本文中，应用局部径向基函数 (RBF) 方法来获得给定有界域上二维 Klein-Gordon 方程解的全局近似。我们使用统一的 RBF 分区 (RBF-PU) 方法，该方法基于将原始域划分为多个补丁并在每个局部域上使用 RBF 近似。与原始（全局）RBF 技术相比，该方法的主要优点是计算成本低和条件良好的最终线性系统。数值实验表明，可以以合理的精度成功解决给定的问题。