کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
767229 897162 2011 9 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
The essence of the generalized Taylor theorem as the foundation of the homotopy analysis method
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی مکانیک
پیش نمایش صفحه اول مقاله
The essence of the generalized Taylor theorem as the foundation of the homotopy analysis method
چکیده انگلیسی

The generalized Taylor theorem is the foundation of the homotopy analysis method proposed by Liao. This theorem is interesting but hard to understand from the mathematical point of view. Especially, there is a key parameter h whose meaning is still unknown. In the paper, we derive the generalized Taylor theorem from a usual way, that is, we prove that the generalized Taylor expansion is equivalent to a different representation of the usual Taylor expansion at different points. Therefore the meaning of the auxiliary parameter h is clarified. These results give a reasonable explanation of the parameter h and uncover the essence of the generalized Taylor theorem from which we can deeply understand the homotopy analysis method. Through the detailed analysis of some examples, we compare the series solution at the different points with the generalized Taylor series solution obtained by the homotopy analysis method.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Communications in Nonlinear Science and Numerical Simulation - Volume 16, Issue 3, March 2011, Pages 1254–1262
نویسندگان
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