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
موضوعات مرتبط
مهندسی و علوم پایه شیمی شیمی تئوریک و عملی
پیش نمایش صفحه اول مقاله
A new high efficient and high accurate Obrechkoff four-step method for the periodic nonlinear undamped Duffing's equation
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, H02∼16.33. 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 5×10−13, 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 (10−11), to below 10−14.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computer Physics Communications - Volume 165, Issue 2, 15 January 2005, Pages 110-126
نویسندگان
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