Series Expansion Method

2015 ◽  
pp. 63-83
Author(s):  
Matthew N. O. Sadiku ◽  
Sudarshan R. Nelatury
Keyword(s):  
Series Expansion ◽  
Expansion Method ◽  
Series Expansion Method

scholarly journals Introduction of the Phone-Concept Into Pole Figure Inversion Using the Iterative Series Expansion Method

1992 ◽  
Vol 19 (3) ◽  
pp. 169-174 ◽  
Author(s):  
M. Dahms
Keyword(s):  
Texture Analysis ◽  
Pole Figure ◽  
Series Expansion ◽  
Expansion Method ◽  
Probabilistic Methods ◽  
Series Expansion Method

The phone-concept as it is used in the various kinds of probabilistic methods can easily be applied to the iterative series expansion method for quantitative texture analysis. Only slight modifications of the existing routines are necessary. The advantages of this concept are demonstrated by a mathematical and an experimental example.

scholarly journals COMPARISON OF A GENERAL SERIES EXPANSION METHOD AND THE HOMOTOPY ANALYSIS METHOD

2010 ◽  
Vol 24 (15) ◽  
pp. 1699-1706 ◽  
Author(s):  
CHENG-SHI LIU ◽  
YANG LIU
Keyword(s):  
Series Expansion ◽  
Homotopy Analysis Method ◽  
Nonlinear Differential Equations ◽  
Expansion Method ◽  
Basis Functions ◽  
Analysis Method ◽  
Convergence Region ◽  
General Series ◽  
Homotopy Analysis ◽  
Series Expansion Method

A simple analytic tool, namely the general series expansion method, is proposed to find the solutions for nonlinear differential equations. A set of suitable basis functions [Formula: see text] is chosen such that the solution to the equation can be expressed by [Formula: see text]. In general, t0 can control and adjust the convergence region of the series solution such that our method has the same effect as the homotopy analysis method proposed by Liao, but our method is simpler and clearer. As a result, we show that the secret parameter h in the homotopy analysis methods can be explained by using our parameter t0. Therefore, our method reveals a key secret in the homotopy analysis method. For the purpose of comparison with the homotopy analysis method, a typical example is studied in detail.

scholarly journals Laplace transform series expansion method for solving the local fractional heat-transfer equation defined on Cantor sets

2016 ◽  
Vol 20 (suppl. 3) ◽  
pp. 777-780
Author(s):  
Huan Sun ◽  
Xing-Hua Liu
Keyword(s):  
Heat Transfer ◽  
Laplace Transform ◽  
Series Expansion ◽  
Transfer Equation ◽  
Expansion Method ◽  
Cantor Sets ◽  
Heat Transfer Equation ◽  
Local Fractional Calculus ◽  
The Laplace Transform ◽  
Series Expansion Method

In this paper, we use the Laplace transform series expansion method to find the analytical solution for the local fractional heat-transfer equation defined on Cantor sets via local fractional calculus.

scholarly journals The local fractional series expansion solution for local fractional Korteweg-de Vries equation

2016 ◽  
Vol 20 (suppl. 3) ◽  
pp. 863-866
Author(s):  
Wei Zhang ◽  
Kai-Li Xu ◽  
Yun Lei
Keyword(s):  
Series Expansion ◽  
Series Solution ◽  
Vries Equation ◽  
Expansion Method ◽  
De Vries ◽  
Series Expansion Method

In this paper, the local fractional series expansion method is used to find the series solution for the local fractional Korteweg-de Vries equation.

A series expansion method aided design of CCII controller for a TITO system

2018 ◽  
Vol 24 (9) ◽  
pp. 3843-3849 ◽  
Author(s):  
Vijay Kumar Verma ◽  
Rajeev Kumar Ranjan ◽  
Pooja Gupta ◽  
Bindu Priyadarshini ◽  
Vijay Nath
Keyword(s):  
Series Expansion ◽  
Expansion Method ◽  
Aided Design ◽  
Series Expansion Method
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