2023/08/23 by L.G.S. Duarte, Duarte, L. G. S., L.A.C.P. da Mota +3
Mathematics · Physics and Astronomy · #34-xx #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #G.1.7 #I.1 #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2308.12391
openalex publication_date 2023/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We have already dealt with the problem of solving First Order Differential Equations (1ODEs) presenting elementary functions before in [1, 2]. In this present paper, we have established solid theoretical basis through a relation between the 1ODE we are dealing with and a rational second order ordinary differential equation, presenting a Liouvillian first Integral. Here, we have expanded the results in [3], where we have establish a theoretical background to deal with rational second order ordinary differential equations (2ODEs) via the S-function method. Using this generalisation and other results hereby introduced, we have produced a method to integrate the 1ODE under scrutiny. Our methods and algorithm are capable to deal efficiently with chaotic systems, determining regions of integrability.