The fictitious boundary surrounding the domain is required in the implementation of the method of fundamental solutions (MFS). A similar approach of taking a portion of the centres of radial basis functions (RBFs) outside the domain in the context of the method of particular solutions (MPS) is proposed to further improve the performance of a two-step MPS-MFS method. Since the shape parameter of RBFs is problem dependent, several known procedures on how to determine a good shape parameter are introduced for solving various types of problems. The proposed method is not only highly accurate but also fairly stable due to the use of the particular solutions and fundamental solutions. To demonstrate the effectiveness of the proposed method, five numerical examples in highly complicate and irregular domains, which include second and fourth order elliptic partial differential equations in 2D and 3D, are presented.

在实施基本解决方案（MFS）时，需要围绕域的虚拟边界。提出了一种在特定解决方案（MPS）方法的上下文中采用径向基函数（RBF）的一部分在域外的方法，以进一步改善两步MPS-MFS方法的性能。由于RBF的形状参数取决于问题，因此引入了几种有关如何确定良好形状参数的已知过程来解决各种类型的问题。由于使用了特定的解决方案和基本解决方案，因此所提出的方法不仅非常准确，而且还相当稳定。为了证明该方法的有效性，在高度复杂和不规则域中使用了五个数值示例，