RT info:eu-repo/semantics/article T1 A modified Lyapunov method and its applications to ODE A1 Lara, Luis Pedro A1 Gadella Urquiza, Manuel K1 Lyapunov method K1 Ordinary differential equations K1 Nonlinear equations K1 22 Física K1 12 Matemáticas AB Here, we propose a method to obtain local analytic approximate solutions of ordinary differential equations with variable coefficients, or even some nonlinear equations, inspired in the Lyapunov method, where instead of polynomial approximations, we use truncated Fourier series with variable coefficients as approximate solutions. In the case of equations admitting periodic solutions, an averaging over the coefficients gives global solutions. We show that, under some restrictive condition, the method is equivalent to the Picard-Lindelöf method. After some numerical experiments showing the efficiency of the method, we apply it to equations of interest in physics, in which we show that our method possesses an excellent precision even with low iterations. PB Wiley SN 0170-4214 YR 2022 FD 2022 LK https://uvadoc.uva.es/handle/10324/55664 UL https://uvadoc.uva.es/handle/10324/55664 LA eng NO Mathematical Methods in the Applied Sciences, 2022. NO Producción Científica DS UVaDOC RD 29-mar-2024