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An accelerated differential equation system with Yosida regularization and its numerical discretized scheme, for solving solutions to a generalized equation, are investigated. Given a maximal monotone operator T on a Hilbert space, this paper will study the asymptotic behavior of the solution trajectories of the differential equation x ˙ (t) + T λ (t) (x (t) − α (t) T λ (t) (x (t))) = 0 , t ≥ t 0 ≥ 0 , to the solution set T − 1 (0) of a generalized equation 0 ∈ T (x). With smart choices of parameters λ (t) and α (t) , we prove the weak convergence of the trajectory to some point of T − 1 (0) with ‖ x ˙ (t) ‖ ≤ O (1 / t) as t → + ∞. Interestingly, under the upper Lipshitzian condition, strong convergence and faster convergence can be obtained. For numerical discretization of the system, the uniform convergence of the Euler approximate trajectory x h (t) → x (t) on interval [ 0 , + ∞) is demonstrated when the step size h → 0. [ABSTRACT FROM AUTHOR]