Abstract
A new kind of Obrechkoff two-step method with Fourier spectrum for the numerical solution of undamped Duffing equation is constructed in this paper. This kind of Obrechkoff two-step method is based on a new family of Obrechkoff two-step method which incorporates odd order derivatives to improve the accuracy, and is derived by the Fourier-fitting technique. The stability analysis and error analysis are carried out. The numerical results confirm our analyses and demonstrate that the new kind of method has great advantages in accuracy, efficiency and stability.
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