2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/124135Although implicit-explicit (IMEX) methods for approximating solutions to semilinear parabolic equations are relatively standard, most recent works examine the case of a fully discretized model. We show that by discretizing time only, one can obtain an elementary convergence result for an implicit-explicit method. This convergence result is strong enough to imply existence and uniqueness of solutions to a class of semilinear parabolic equations.10 pagesAnalysis of PDEs34G20 (Primary); 34G25; 35K57; 65J15; 34K30 (Secondary)text