Stability estimate on meshless unsymmetric collocation method for solving boundary value problems

Y. Duan; Y.C. Hon; W. Zhao

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Stability estimate on meshless unsymmetric collocation method for solving boundary value problems

机译：求解边值问题的无网格非对称搭配方法的稳定性估计

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摘要

We investigate in this paper the stability of meshless unsymmetric collocation method by using radial basis functions for solving boundary value problems under Dirichlet, Neumann, or Robin boundary conditions. Using the monotonically decreasing property of the Fourier transforms of RBFs, we prove that the lowest bound of the resultant linear system depends on the separation distance of distinct centers and the decreasing order of the RBFs. Stability estimates can then be obtained for the meshless unsymmetric collocation method. For verification, several numerical examples are constructed to verify the theoretical results.

机译：我们通过使用径向基函数解决Dirichlet，Neumann或Robin边界条件下的边值问题，研究了无网格非对称配置方法的稳定性。利用RBFs的傅立叶变换的单调递减性质，我们证明了所得线性系统的最低边界取决于不同中心的分离距离和RBFs的递减顺序。然后可以为无网格不对称搭配方法获得稳定性估计。为了验证，构建了几个数值示例来验证理论结果。

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来源
《Engineering analysis with boundary elements》 |2013年第4期|666-672|共7页
作者
Y. Duan; Y.C. Hon; W. Zhao;
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作者单位

School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, P.R. China;

Department of Mathematics, City University of Hong Kong, Hong Kong;

School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, P.R. China;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
stability; radial basis functions; unsymmetric collocation method; boundary value problems;

机译：稳定性;径向基函数;不对称搭配法边值问题;

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专利

1. CONVERGENCE OF UNSYMMETRIC KERNEL-BASED MESHLESS COLLOCATION METHODS [J] . ROBERT SCHABACK SIAM Journal on Numerical Analysis . 2008,第1期

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2. Convergence of unsymmetric kernel-based meshless collocation methods [J] . Schaback R SIAM Journal on Numerical Analysis . 2007,第1期

机译：基于非对称核的无网格搭配方法的收敛性
3. Essential boundary condition enforcement in meshless methods: boundary flux collocation method [J] . Cheng-Kong C. Wu, Michael E. Plesha International Journal for Numerical Methods in Engineering . 2002,第3期

机译：无网格方法中基本边界条件的实施：边界通量配置方法
4. On the treatment of Neumann boundary conditions in collocation-based meshless methods [C] . Xiang-dong Zhang, Lei Wang, Da-wei Teng International Conference on Applied Mechanics, Materials and Manufacturing . 2013

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5. Meshless collocation methods for the numerical solution of elliptic boundary valued problems the rotational shallow water equations on the sphere. [D] . Blakely, Christopher D. 2009

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6. A hybrid collocation method for solving highly nonlinear boundary value problems [O] . A.O. Adewumi, S.O. Akindeinde, A.A. Aderogba, 2020

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7. Stable and convergent unsymmetric meshless collocation methods [O] . Leevan Ling, Robert Schaback 2006

机译：稳定和收敛的非对称无网格搭配方法
8. Alternating Direction Implicit Orthogonal Spline Collocation Methods for Solving Initial/Boundary Value Problems [R] . Bialecki, B. , Fairweather, G. 1998

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Stability estimate on meshless unsymmetric collocation method for solving boundary value problems

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