A symbolic-numeric method to analyse nonlinear differential equations in Fourier domain

Authors:
Nicolas Ratier;Mickael Bruniaux
Affiliations:
Institut FEMTO-ST, Département LPMO, Ecole Nationale Supérieure de Mécanique et des Microtechniques, Besançon Cedex, France;Institut FEMTO-ST, Département LPMO, Ecole Nationale Supérieure de Mécanique et des Microtechniques, Besançon Cedex, France
Venue:
MMACTE'05 Proceedings of the 7th WSEAS International Conference on Mathematical Methods and Computational Techniques In Electrical Engineering
Year:
2005

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Abstract

This paper presents a method to express, in symbolic form, any system of algebrico-differential equations into a nonlinear system of Fourier coefficient of the unknowns. The solution of the nonlinear equations generated in the last step of the method gives an approximation of the steady-state solution of the differential equations. Main applications should be found in the domain of ultra-stable oscillator circuits. The paper explains how to face with the two main difficulties of this symbolic computation: the processing of the nonlinear components and the control of the large number of coefficients. The solution proposed is inspired from compiler construction techniques.