The identification of continuous-time systems from discrete-time data is investigated in a bounded-error context. Errors are taken as a discrete time signal, additive on output, unknown but bounded with known bounds. The set inversion via interval analysis algorithm is used with validated numerical integration methods. The theory of monotone cooperative systems is also introduced in order to derive tighter enclosures for the solution of the differential equations. Via an illustrative example with simulated data, it is shown that for systems modelled by parabolic differential equations, the cooperativity property only makes it possible to obtain results in a reasonable computation time.