中文摘要：

把一种真正的无网格局部Petrov—Galerkin方法用于求解非线性边值问题．为了克服一般局部Petrov—Galerkin方法计算工作量较大的问题，选择一个分段函数作为加权残值法的加权函数，简化了非线性问题中刚度矩阵的域积分．基于局部Petrov—Galerkin积分方程逐点建立的思想，推导了一种直接插值法用于施加本质边界条件．通过算例表明，这种局部Petrov—Galerkin方法是一种具有收敛快、精度高的方法．

英文摘要：

A truly meshless local Petrov-Galerkin （MLPG） method was presented to solve nonlinear boundary value problems. A simple Heaviside test function was chosen to overcome the computationally expensive problems. The computational effort was significantly reduced by simplifying the domain integral for the stiffness matrix in the MLPG method. Due to the MLPG method which establishes equations node by node, a direct interpolation method was proposed to impose essential boundary conditions. Numerical results show that the proposed method possesses high rates of convergence for the Sobolev norms with reasonably accurate results.