Localized meshless methods based on polynomial basis functions for solving axisymmetric equations

摘要

In this paper, two localized meshless methods based on polynomial basis functions are utilized to solve axisymmetric problems. In the first approach, we applied the localized method of particular solutions (LMPS) and the closed-form particular solution to simplify the two-stage approach using Chebyshev polynomial as the basis functions for solving axisymmetric problems. We also propose the modified local Pascal polynomial method (MLPM) to compare the results with LMPS. Since only the low order polynomial basis functions are used, no preconditioning treatment is required and the solution is quite stable. Four numerical examples are given to demonstrate the effectiveness of the proposed methods.