应用局部近似特别解方法求解一类偏微分方程  

Local Method of Approximate Particular Solutions for a Class of Partial Differential Equations

作　　者：丁亮[1] 张学莹[1] 

机构地区：[1]河海大学理学院,江苏南京210098

出　　处：《江南大学学报（自然科学版）》2014年第2期232-236,共5页Joural of Jiangnan University (Natural Science Edition)　

摘　　要：针对传统的有网格方法,在求解偏微分方程时很大程度上依赖网格划分的质量,有时会导致计算失败的问题。提出了一种无网格方法——局部近似特别解方法。该方法需要建立一个支持域,利用支持域内的点构造一个低阶线性方程组,通过求解这个低阶线性方程组可以得到线性组合系数,然后推广到全局形成一个大型稀疏线性方程组,从而直接求解这个线性方程组而不需要复杂的迭代过程。数值实验表明,局部近似特别解方法在解决一类偏微分方程时有较高的精度和效率。In the solution of partial differential equations, there is a grid method, such as the finite element method and the finite boundary method,relying heavily on the quality of the mesh, and sometimes it leads to fail. We propose a meshless method-the local method of approximate particular solution （LMAPS） and need to create a support region within a few points and try to solve the resultant low order linear system for obtaining the coefficients of equations. Then we reformulate a global large sparse system of equations. Directly,not using the complicated iterative method. The nmnerical experiments have shown that LMAPS is suitable to solve a class of partial differential equations with high accuracy and efficiency.

关 键 词：偏微分方程 Navier-Stokys方程 径向基函数 LMAPS法 

分 类 号：O242.1[理学—计算数学] O302[理学—数学]