Diffraction of light by superposed parallel supersonic waves, one being then-th harmonic of the other. Solution of the system of difference-differential equations for the amplitudes by a series expansion method

1971 ◽  
Vol 73 (5) ◽  
pp. 232-239 ◽  
Author(s):  
Oswald Leroy
Keyword(s):  
Differential Equations ◽  
Series Expansion ◽  
Expansion Method ◽  
The Other ◽  
Diffraction Of Light ◽  
Series Expansion Method

scholarly journals Local Fractional Series Expansion Method for Solving Wave and Diffusion Equations on Cantor Sets

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Ai-Min Yang ◽  
Xiao-Jun Yang ◽  
Zheng-Biao Li
Keyword(s):  
Differential Equations ◽  
Series Expansion ◽  
Analytical Solutions ◽  
Fractional Derivatives ◽  
Expansion Method ◽  
Cantor Sets ◽  
Diffusion Equations ◽  
And Diffusion ◽  
Series Expansion Method

We proposed a local fractional series expansion method to solve the wave and diffusion equations on Cantor sets. Some examples are given to illustrate the efficiency and accuracy of the proposed method to obtain analytical solutions to differential equations within the local fractional derivatives.

scholarly journals Application of Local Fractional Series Expansion Method to Solve Klein-Gordon Equations on Cantor Sets

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Ai-Min Yang ◽  
Yu-Zhu Zhang ◽  
Carlo Cattani ◽  
Gong-Nan Xie ◽  
Mohammad Mehdi Rashidi ◽  
...  
Keyword(s):  
Differential Equations ◽  
Series Expansion ◽  
Analytical Solutions ◽  
Fractional Derivatives ◽  
Expansion Method ◽  
Cantor Sets ◽  
Present Technique ◽  
Klein Gordon ◽  
Series Expansion Method

We use the local fractional series expansion method to solve the Klein-Gordon equations on Cantor sets within the local fractional derivatives. The analytical solutions within the nondifferential terms are discussed. The obtained results show the simplicity and efficiency of the present technique with application to the problems of the liner differential equations on Cantor sets.

Fractional series expansion method for fractional differential equations

2015 ◽  
Vol 25 (7) ◽  
pp. 1525-1530 ◽  
Author(s):  
Zheng-Biao Li ◽  
Wei-Hong Zhu
Keyword(s):  
Differential Equations ◽  
Series Expansion ◽  
Fractional Differential Equations ◽  
Expansion Method ◽  
Kantorovich Method ◽  
Content Type ◽  
Analytical Technique ◽  
Liouville Derivative ◽  
Fractional Differential ◽  
Series Expansion Method

Purpose – The purpose of this paper is to suggest a new analytical technique called the fractional series expansion method for solving linear fractional differential equations (FDEs). Design/methodology/approach – This method is based on the idea of Kantorovich method, convergent series, and the modified Riemann-Liouville derivative. Findings – This work suggests a new analytical technique. The FDEs are described in Jumarie’s sense. Originality/value – It finds a new method for solving linear FDEs. The solution procedure is elucidated by two examples.

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.

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