Approximate solutions for the nonlinear duffing oscillator with an external force

[摘要] This paper is concerned with a finding of an approximate solution to the Duffing oscillator with a linear external force using a modified differential transform method (MDTM) and Runge-Kutta-Nystrom (RKN) method. The results obtained from the two methods are then numerically and graphically compared. We found that both results are close to one another when an amplitude and frequency of external forces are very small. However, both results are quite different when the amplitude and frequency of external forces are large. Their results are in agreement with the phase plane diagram which demonstrates a stable equilibrium point for both methods in case of small amplitude and frequency of external force. However, for large amplitude and frequency of external forces, only MDTM shows the stable equilibrium point.

[发布机构] Department of Mathematics, Faculty of Scinece, King Mongkut's Institute of Technology Ladkrabang, Thailand^1

[效力级别] 数学

[关键词] Approximate solution;Differential transform method;Duffing oscillator;External force;Large amplitude;Phase plane;Small amplitude;Stable equilibrium points