A class of ergodic solutions of nonlinear differential equations and numerical treatment

In this paper, we give existence theorems of a class of ergodic solutions, pseudo almostperiodic solutions, for nonlinear differential equations. Based on these, a useful numerical method of such kind of solutions for nonlinear differential equations is established. A numerical example of the ergodic type nonlinear oscillation equation is illustrated by both the symplectic scheme and the method of computing initial value for the pseudo almost-periodic solution.