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

International audienceThis 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