2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/138957Purely numerical methods do not always provide an accurate way to find all the global solutions to nonlinear ODE on infinite intervals. For example, finite-difference methods fail to capture the asymptotic behavior of solutions, which might be critical for ensuring global existence. We first show, by way of a detailed example, how asymptotic information alone provides significant insight into the structure of global solutions to a nonlinear ODE. Then we propose a method for providing this missing asymptotic data to a numerical solver, and show how the combined approach provides more detailed results than either method alone.30 pages, 12 figuresClassical Analysis and ODEs34E05;34B40text