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LMAPS for solving fourth-order PDEs with polynomial basis functions
Mathematics and Computers in Simulation ( IF 4.6 ) Pub Date : 2020-11-01 , DOI: 10.1016/j.matcom.2020.05.013
C.S. Chen , Shu-Hui Shen , Fangfang Dou , J. Li

Abstract Due to certain difficulties in solving fourth-order partial differential equations (PDEs) using localized methods, the given differential equation is normally split into two decoupled second order PDEs. Such an approach is only feasible for Dirichlet and Laplace boundary conditions. In this paper the localized method of particular solutions is applied to fourth-order PDEs directly using polynomial basis functions. The effectiveness of the proposed algorithms is demonstrated by considering four numerical examples.

中文翻译:

LMAPS 用于求解具有多项式基函数的四阶偏微分方程

摘要 由于局部方法求解四阶偏微分方程(PDE)存在一定的困难,通常将给定的微分方程分解为两个解耦的二阶偏微分方程。这种方法仅适用于 Dirichlet 和 Laplace 边界条件。在本文中,特定解的局部化方法直接使用多项式基函数应用于四阶偏微分方程。通过考虑四个数值例子证明了所提出算法的有效性。
更新日期:2020-11-01
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