a pseudospectral method for nonlinear duffing equation ：非线性duffing方程的拟谱方法.pdfVIP

Research Article Received 13 February 2013 Published online in Wiley Online Library () DOI: 10.1002/MMA.3142 MOS subject classification: 65M70; 34B15; 41A10 A pseudospectral method for nonlinear Duffing equation involving both integral and non-integral forcing terms Abbas Saadatmandia*† and Fateme Mashhadi-Finia Communicated by S. Wise The Legendre pseudospectral method is developed for the numerical solution of nonlinear Duffing equation involving both integral and non-integral forcing terms. By using differentiation matrix, the problem is reduced to the solution of a system of algebraic equations. The method is general, easy to implement, and yields very accurate results. Numerical experiments are presented to demonstrate the accuracy and the efficiency of the proposed computational procedure. Copyright © 2014 John Wiley Sons, Ltd. Keywords: Duffing equation; pseudospectral method; collocation method; Legendre–Gauss–Lobatto; integral equation 1. Introduction It is well known that Duffing equation is a mathematical model for describing a classical oscillator in a single-well or double-well potential with a periodic driving force and has been widely investigated in chaotic phenomena [1, 2]. This equation is used to discuss some important practical phenomena such as orbit extraction, nonuniformity caused by an infinite domain, nonlinear mechanical oscillators, and prediction of diseases. [3–8]. In this paper, we consider the following Duffing equation involving both integral and non-integral forcing terms 00 0 0 Z x y .x / C y .x / C f .x , y .x /, y .x // C k.x , t, y .t//dt D 0, 0 x 1, (1)