Article (Scientific journals)
Meshfree collocation method for implicit time integration of ODEs
Netuzhylov, H.; Zilian, Andreas
2011In International Journal of Computational Methods, 8 (1), p. 119-137
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Keywords :
Lorenz equations; Meshfree; Interpolating moving least squares; Lorenz equation; Meshless; Integral equations; Integration; Interpolation; Least squares approximations; Ordinary differential equations; Stability; Nonlinear equations
Abstract :
[en] An implicit time integration meshfree collocation method for solving linear and nonlinear ordinary differential equations (ODEs) based on interpolating moving least squares technique, which uses singular weights for constructing ansatz functions, is presented. On an example of a system of equations for Foucault pendulum, the flexibility of the proposed approach is shown and the accuracy, convergence, and stability properties are investigated. In a nonlinear case, the method gives accurate results, which is demonstrated by the solution of Lorenz equations. The typical trajectory patterns, e.g. butterfly pattern, were observed and the properties of the method are compared to those of a higher-order time integration method. © 2011 World Scientific Publishing Company.
Disciplines :
Mathematics
Author, co-author :
Netuzhylov, H.;  Technische Universität Braunschweig, Computational Sciences in Engineering (CSE), Beethovenstr. 51, 38106 Braunschweig, Germany
Zilian, Andreas  ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit
Language :
English
Title :
Meshfree collocation method for implicit time integration of ODEs
Publication date :
2011
Journal title :
International Journal of Computational Methods
ISSN :
0219-8762
Publisher :
World Scientific Publishing Co., Singapore
Volume :
8
Issue :
1
Pages :
119-137
Peer reviewed :
Peer Reviewed verified by ORBi
Focus Area :
Computational Sciences
Available on ORBilu :
since 18 November 2013

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