کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
10350212 | 863819 | 2005 | 17 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A new high efficient and high accurate Obrechkoff four-step method for the periodic nonlinear undamped Duffing's equation
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موضوعات مرتبط
مهندسی و علوم پایه
شیمی
شیمی تئوریک و عملی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Based on the idea of the previous Obrechkoff's two-step method, a new kind of four-step numerical method with free parameters is developed for the second order initial-value problems with oscillation solutions. By using high-order derivatives and apropos first-order derivative formula, the new method has greatly improved the accuracy of the numerical solution. Although this is a multistep method, it still has a remarkably wide interval of periodicity, H02â¼16.33. The numerical test to the well known problem, the nonlinear undamped Duffing's equation forced by a harmonic function, shows that the new method gives the solution with four to five orders higher than those by the previous Obrechkoff's two-step method. The ultimate accuracy of the new method can reach about 5Ã10â13, which is much better than the one the previous method could. Furthermore, the new method shows the great superiority in efficiency due to a reasonable arrangement of the structure. To finish the same computational task, the new method can take only about 20% CPU time consumed by the previous method. By using the new method, one can find a better 'exact' solution to this problem, reducing the error tolerance of the one widely used method (10â11), to below 10â14.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computer Physics Communications - Volume 165, Issue 2, 15 January 2005, Pages 110-126
Journal: Computer Physics Communications - Volume 165, Issue 2, 15 January 2005, Pages 110-126
نویسندگان
Yongming Dai, Zhongcheng Wang, Deying Zhao, Xiaolong Song,