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 24-nov-2024