2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76709We propose a method for obtaining rigorous and accurate upper and lower bounds on the eigenvalues of ordinary and partial differential operators in bounded regions of Euclidean space. It uses a boundary condition homotopy method starting from a decomposition of the region into several simpler regions for which the eigenvalues can already be computed accurately. Several numerical examples are presented.Spectral TheoryAnalysis of PDEs34L15 ; 35P15 ; 49R05 ; 49R10 ; 65L15 ; 65L60 ; 65L70 ; 65N25text