Available online at www.isr-publications.com/jnsa J. Nonlinear Sci. Appl., 11 (2018), 1331–1336 Research Article Journal Homepage: www.isr-publications.com/jnsa Using differentiation matrices for pseudospectral method solve Duffing Oscillator L. A. Nhat PhD student of RUDN University, Moscow 117198, Russia. And Lecture at Tan Trao University, Tuyen Quang province, Vietnam. Communicated by R. Saadati Abstract This article presents an approximate numerical solution for nonlinear Duffing Oscillators by pseudospectral (PS) method to compare boundary conditions on the interval [-1, 1]. In the PS method, we have been used differentiation matrix for Chebyshev points to calculate numerical results for nonlinear Duffing Oscillators. The results of the comparison show that this solution had the high degree of accuracy and very small errors. The software used for the calculations in this study was Mathematica V.10.4. Keywords: Duffing oscillator, pseudospectral methods, differential matrix, Duffing system, Chebyshev points. 2010 MSC: 34B15, 41A50, 65L10. c 2018 All rights reserved. 1. Introduction In science and engineering, the Duffing Oscillator was a common model for nonlinear phenomena. The most general forced form of the Duffing equation is: ∂ 2 ∂t 2 x(t)+ α ∂ ∂t x(t)+ βx(t) 3 + γx(t)= δ cos(θt), -1  t  1, x(-1)= 0, x(1)= 0, (1.1) where α, β, γ, δ, θ are parameters: α controls the amount of damping; β controls the amount of non- linearity in the restoring force; γ controls the linear stiffness; δ is the amplitude of the periodic driving force; θ is the angular frequency of the periodic driving force. Equation (1.1) depends on the different γ,β, we had some special cases: γ> 0, β> 0: Hard Spring Duffing Oscillator; γ> 0, β< 0: Soft Spring Duffing Oscillator; γ< 0, β> 0: Inverted Duffing Oscillator; ∗ Corresponding author Email address: leanhnhat@tuyenquang.edu.vn (L. A. Nhat) doi: 10.22436/jnsa.011.12.04 Received: 2018-06-17 Revised: 2018-08-05 Accepted: 2018-08-19