Meshless collocation: Error estimates with application to dynamical systems

被引：59
作者：
Giesl, Peter
Wendland, Holger
机构：
[1] Tech Univ Munich, Zentrum Math, D-85747 Garching, Germany
[2] Univ Sussex, Dept Math, Brighton BN1 9RF, E Sussex, England
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 2007年 / 45卷 / 04期
关键词：
partial differential equation; radial basis function; error estimates; Lyapunov function;
D O I：
10.1137/060658813
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we derive error estimates for generalized interpolation, in particular collocation, in Sobolev spaces. We employ our estimates in collocation problems using radial basis functions and extend and improve previously known results for elliptic problems. Finally, we use meshless collocation to approximate Lyapunov functions for dynamical systems.
引用
收藏
页码：1723 / 1741
页数：19
相关论文
共 28 条
[1]  
Adams R., 1975, Sobolev Spaces
[2]  
[Anonymous], SURFACE FITTING MULT
[3]  
Brenner S. C., 2007, Texts Appl. Math., V15
[4]  
Buhmann MD., 2003, Cambridge Monogr. Appl. Comput. Math
[5]  
Fasshauer GE, 1999, BOUNDR ELEMENT, V2, P291
[6]   Solving partial differential equations by collocation using radial basis functions [J].
Franke, C ;
Schaback, R .
APPLIED MATHEMATICS AND COMPUTATION, 1998, 93 (01) :73-82
[7]   Convergence order estimates of meshless collocation methods using radial basis functions [J].
Franke, C ;
Schaback, R .
ADVANCES IN COMPUTATIONAL MATHEMATICS, 1998, 8 (04) :381-399
[8]  
Giesl P, 2007, LECT NOTES MATH, V1904, P1, DOI 10.1007/978-3-540-69909-5
[9]  
GIESL P, 2004, P NOLCOS 2004 C STUT, V2, P865
[10]   Stepwise calculation of the basin of attraction in dynamical systems using radial basis functions [J].
Giesl, Peter .
Algorithms for Approximation, Proceedings, 2007, :113-122
123