Refined least squares approach to the initial-value problems unstable in the Lyapunov sense

• Autorzy: Walentyński R.
• Języki publikacji: EN

Abstrakty

EN

The paper presents application of the Refined Least Squares method to the initial value problems that are instable in the Lyapunov sense. There is shown that the method is not sensitive to this kind of instability. The method is especially useful in search of particular integral of the considered problem. The method has an additional tool to evaluate quality of approximation. The approach is based on minimization of the functional, which square root can is generalized norm L-2 and can be used to estimate global error of approximation. The expected value of the functional is equal to zero. The approximation is satisfactory if both results converge and functional reaches value close to zero. The consideration is illustrated with examples. There are shown initial-value problems which have physical sense and are applicable in mechanics. Whereas numerical approach may fail for these tasks, Refined Least Squares approach returns reliable approximation. The last example presents application of the special feature of the method, which allows neglecting influence of general integral on the solution. The method may be used in sensitivity analysis, search of the problem parameters, verification of numerical methods and an antonymous method in computational physics and mechanics.

Słowa kluczowe

EN

Refined Least Squares method; initial-value problems; Lyapunov method

PL

mechanika; metoda Ljapunowa

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Mechanics and Engineering Sciences
• Rocznik: 2005
• Tom: Vol. 12, No. 1
• Strony: 65--81
• Opis fizyczny: Bibliogr. 8 poz., wykr.

Twórcy

autor

Walentyński R.

• Silesian University of Technology, Faculty of Civil Engineering [Politechnika Ślaska], Akademicka 5, 44-101 Gliwice

Bibliografia

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• [4] R. A. Walentyński, Computer assisted analytical solution of initial-boundary value problems. In: Computer Methods in Mechanics, Proceedings of the 13th PCCMM, A. Garstecki and J. Rakowski, eds. Poznań University of Technology, Poznań, pp. 1363-1400, 1997.
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• [6] R. A. Walentyński, Dealing with shell’s boundary conditions with the refined least squares method. Proceedings of the 5th World Congress on Computational Mechanics (WCCM V), H. A. Mang, F. G. Rammerstorfer and J. Eberhardsteiner, eds. Vienna University of Technology, Vienna, pp. 10, 2002 http://wccm.tuwien.ac.at/publications/Papers/fp80303.pdf
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