کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4976507 1365645 2009 14 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
An extension of the general Struble's method for solving an nth order nonlinear differential equation when the corresponding unperturbed equation has some repeated eigenvalues
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر پردازش سیگنال
پیش نمایش صفحه اول مقاله
An extension of the general Struble's method for solving an nth order nonlinear differential equation when the corresponding unperturbed equation has some repeated eigenvalues
چکیده انگلیسی
This paper attempts to show the more suitability of the extended general Struble's technique than the unified Krylov-Bogoliubov-Mitropolskii (KBM) method in solving the problems that occur during the critical conditions. Recently a critically damped condition of an nth, n=2,3, … order weakly nonlinear autonomous ordinary differential equation has been investigated by the unified KBM method, in which the corresponding unperturbed equation has some real (negative) repeated eigenvalues. But there are more important critical conditions, which are still untouched. One of them occurs when a pair of complex eigenvalues is equal to another. It is complicated to formulate as well as to utilize the KBM method to investigate this condition. However, the extended general Struble's technique is applicable to both autonomous and non-autonomous systems. Solutions obtained for different critical conditions as well as for different initial conditions show a good agreement with the numerical solutions. The method is illustrated by an example of a fourth-order nonlinear differential equation whose unperturbed equation has repeated complex eigenvalues. A steady-state solution is determined for the non-autonomous equation. Moreover, a critical condition of a fourth-order nonlinear equation is investigated when two real eigenvalues of the unperturbed equation are non-positive and equal.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of the Franklin Institute - Volume 346, Issue 2, March 2009, Pages 112-125
نویسندگان
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