Articles | Volume 14
https://doi.org/10.5194/ars-14-51-2016
https://doi.org/10.5194/ars-14-51-2016
28 Sep 2016
 | 28 Sep 2016

Adapting the range of validity for the Carleman linearization

Harry Weber and Wolfgang Mathis

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Cited articles

Carleman, T.: Application de la théorie des équations intégrales linéaires aux systèmes d'équations différentielles non linéaires, Acta Mathematica, 1932.
Chua, L. O., Desoer, C. A., and Kuh, E. S.: Linear and Nonlinear Circuits, McGraw-Hill Book Company, 1987.
Kerner, E. H.: Universal formats for nonlinear ordinary differential systems, J. Math. Phys., 22, 1366–1371, 1981.
Kowalski, K.: Nonlinear dynamical systems and classical orthogonal polynomials, J. Math. Phys., 38, 2483–2505, 1997.
Kowalski, K. and Steeb, W.-H.: Nonlinear Dynamical Systems and Carleman Linearization, World Scientific, 1991.
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Short summary
In this contribution, the limitations of the Carleman linearization approach are presented and discussed. The Carleman linearization transforms an ordinary nonlinear differential equation into an infinite system of linear differential equations which cannot be solved in general. Therefore, the infinite dimensional system has to be approximated by a finite one. The idea of this contribution is to use a Taylor series for the approximation of the infinite system.