Finding Periodic Solutions of High Order Duffing Equations via Homotopy Method

Abstract

This paper presents a detailed analysis of finding the periodic solutions for the high order Duffing equation $$x^{(2n)} + g(x) = e(t)   (n≥1).$$Firstly, we give a constructive proof for the existence of periodic solutions via the homotopy method. Then we establish an efficient and global convergence method to find periodic solutions numerically.