In this paper, three meshless methods are proposed to solve boundary value problems. The special purpose Trefftz function method, the method of fundamental solutions and the symmetry method of fundamental solutions are compared. We considered six numerical examples for harmonic and biharmonic problems as a flow through the cylindrical fibers arranged in a regular square array, deflection of a uniformly loaded square plate and torsion of a bar. The boundary value problems defined for a repeating element of the domain are solved by use of the collocation technique. The accuracy and stability of compared methods are investigated. Root mean square error on the boundary and condition number of the matrix are presented as functions of a number of collocation points.

本文提出了三种无网格方法来解决边值问题。比较了专用Trefftz函数方法，基本解的方法和基本解的对称方法。我们考虑了谐波和双谐波问题的六个数值示例，它们是通过以规则正方形阵列排列的圆柱纤维的流动，均匀加载的正方形板的挠度和杆的扭转。通过使用搭配技术可以解决为域的重复元素定义的边值问题。研究了所比较方法的准确性和稳定性。矩阵边界和条件数的均方根误差是多个搭配点的函数。