The modifying generalized moving least squares approximation meshless method and application on plane piezoelectric problem

Meshless method is a new numerical method on problem for determining solution of differential equation. The moving least squares approximation makes only require least squares approximation with regard to functional value at all nodes. It makes no require for the residual of derivative approximation. However, the generalized moving least squares approximation makes require least squares approximation with regard to functional and its derivative value at all nodes. For the sake of decrease the computing time, modifying generalized moving least squares approximation is constructed under adding the residual of high orders derivative only at the portion nodes. The modifying generalized moving least squares approximation has high accuracy not only for function value but also one or higher orders derivative. This method is well applied to plane piezoelectric problem.