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

Authors:
R. P. Agarwal;Jialin Hong;Ying Liu
Affiliations:
Department of Mathematics, National University of Singapore Singapore, 119260 Singapore;Institute of Computational Mathematics and Scientific/Engineering Computing Chinese Academy of Sciences, Beijing 100080, P.R. China;Department of Mathematical Sciences, Tsinghua University Beijing 100084, P.R. China
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2000

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Abstract

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.