scholarly journals New Refinements for the Error Function with Applications in Diffusion Theory

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2017
Author(s):  
Gabriel Bercu
Keyword(s):  
Fourier Series ◽  
Approximation Method ◽  
Diffusion Theory ◽  
Error Function ◽  
Padé Approximation ◽  
Absolute Error ◽  
Series Method ◽  
Pade Approximation ◽  
Fourier Series Method ◽  
The Absolute

In this paper we provide approximations for the error function using the Padé approximation method and the Fourier series method. These approximations have simple forms and acceptable bounds for the absolute error. Then we use them in diffusion theory.

scholarly journals A New Approach of Asymmetric Homoclinic and Heteroclinic Orbits Construction in Several Typical Systems Based on the Undetermined Padé Approximation Method

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Jingjing Feng ◽  
Qichang Zhang ◽  
Wei Wang ◽  
Shuying Hao
Keyword(s):  
Dynamic Systems ◽  
Approximation Method ◽  
Padé Approximation ◽  
Global Bifurcation ◽  
Heteroclinic Orbits ◽  
Symmetric System ◽  
Pade Approximation ◽  
New Approach ◽  
Homoclinic And Heteroclinic Orbits ◽  
Single Orbit

In dynamic systems, some nonlinearities generate special connection problems of non-Z2symmetric homoclinic and heteroclinic orbits. Such orbits are important for analyzing problems of global bifurcation and chaos. In this paper, a general analytical method, based on the undetermined Padé approximation method, is proposed to construct non-Z2symmetric homoclinic and heteroclinic orbits which are affected by nonlinearity factors. Geometric and symmetrical characteristics of non-Z2heteroclinic orbits are analyzed in detail. An undetermined frequency coefficient and a corresponding new analytic expression are introduced to improve the accuracy of the orbit trajectory. The proposed method shows high precision results for the Nagumo system (one single orbit); general types of non-Z2symmetric nonlinear quintic systems (orbit with one cusp); and Z2symmetric system with high-order nonlinear terms (orbit with two cusps). Finally, numerical simulations are used to verify the techniques and demonstrate the enhanced efficiency and precision of the proposed method.

scholarly journals 1-D heat conduction in a fractal medium: A solution by the local fractional Fourier series method

2013 ◽  
Vol 17 (3) ◽  
pp. 953-956 ◽  
Author(s):  
Yuzhu Zhang ◽  
Aimin Yang ◽  
Xiao-Jun Yang
Keyword(s):  
Heat Transfer ◽  
Fourier Series ◽  
Heat Conduction ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Series Method ◽  
Heat Transfer Mechanism ◽  
Basic Properties ◽  
Fractal Medium ◽  
Fourier Series Method

In this communication 1-D heat conduction in a fractal medium is solved by the local fractional Fourier series method. The solution developed allows relating the basic properties of the fractal medium to the local heat transfer mechanism.

Development of the Low Cost Harmonic and Power Instrument by Using Fourier Series Method with Microcontroller

2014 ◽  
Vol 492 ◽  
pp. 519-525
Author(s):  
Napat Watjanatepin ◽  
Chaiyant Boonmee ◽  
Yutthana Kantaphayao
Keyword(s):  
Fourier Series ◽  
Power Factor ◽  
Measurement Errors ◽  
Single Phase ◽  
Low Cost ◽  
Electrical Power ◽  
Quality Measurement ◽  
Series Method ◽  
Electrical Parameters ◽  
Fourier Series Method

The objective of this paper is to present the application of microcontroller dsPIC30F6012A to measure the harmonics current and electrical power by using the Fourier series method to calculate the electrical parameters. This design is to develop the low cost harmonics instrument and to focus on working with the single phase AC system. The prototype was then developed to measure the harmonics current and power factor, and the result was compared with the standard instrument. The result is that most electrical parameters have the measurement errors of less than 4.0%. However, this idea could be developed so that it applies in the related work with the power quality measurement.

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