American Journal of Applied Mathematics and Statistics
ISSN (Print): 2328-7306 ISSN (Online): 2328-7292 Website: http://www.sciepub.com/journal/ajams Editor-in-chief: Mohamed Seddeek
Open Access
Journal Browser
Go
American Journal of Applied Mathematics and Statistics. 2013, 1(4), 76-82
DOI: 10.12691/ajams-1-4-5
Open AccessArticle

Similar Constructing Method for Solving the Boundary Value Problem of the Composite First Weber System

Dong Xiaoxu1, , Li Shunchu1, Gui Dongdong2, Pu Jun1 and Li Huichun3

1School of Mathematics and Computer Engineering, Xihua University, Chengdu, China

2Beijing Dongrunke Petroleum Technology Co., Ltd., Beijing, China

3Geological Research Department of the Fourth Oil Production Plant of DaGang Oilfield Company, Tianjin, China

Pub. Date: September 25, 2013

Cite this paper:
Dong Xiaoxu, Li Shunchu, Gui Dongdong, Pu Jun and Li Huichun. Similar Constructing Method for Solving the Boundary Value Problem of the Composite First Weber System. American Journal of Applied Mathematics and Statistics. 2013; 1(4):76-82. doi: 10.12691/ajams-1-4-5

Abstract

In this paper, we solve a class of boundary value problems of the composite first Weber system. In the process of solving the problem, first of all, we introduce functions of guide solution. Secondly, we constructive similar kernel functions. Finally, solutions with a form of continued fraction product to boundary value problem of the composite first Weber system are obtained by assembling coefficients of the non-homogeneous left boundary condition, functions of guide solution, coefficients of two connection conditions and similar kernel functions. Then a new method is obtained for solving the composite boundary value problem-Similar Constructing Method (shortened as SCM). This method is not only simple and effective for solving the complicated boundary value problem of differential system, but also is a kind of innovative idea.

Keywords:
boundary value problem composite Weber system similar constructing method; similar kernel function function of guide solution

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]  LI Shunchu, YI Liangzhong, Zheng Pengshe. The Similar Structure of Differential Equations on Fixed Solution Problem (in Chinese). Journal of Sichuan University (Natural Science Edition), 2006,43(4):933-934.
 
[2]  JIA Minhui, LI Shunchu. The Similar Structure of Solution Differential Equation on Boundary Value Problem (in Chinese). College Mathematics, 2005,21(5):37-39.
 
[3]  LI Shunchu. The Similar Structure of Solution of Second-order Linear Homogeneous Differential Equations with Constant Coefficients on the Boundary Value Problem (in Chinese). Journal of Xihua University (Natural Science Edition), 2007,26(1):84-85.
 
[4]  LI Shunchu. The Similar Structure of Solution to the Boundary Value Problem for Second-order Linear Homogeneous Differential Equations (in Chinese). Journal of Xihua University (Natural Science Edition), 2009,28(5): 40-41(to 90).
 
[5]  Yan Juan, Li Shunchu, Xing Chenglin. The Similar Structures of Solutions to First Class Boundary Value Problem of Sceond-order Euler Equation (in Chinese). Journal of Xihua University (Natural Science Edition), 2009, 28(6):86-88.
 
[6]  LI Quanyong, LI Shunchu, Chi Ying. The Similar Structure of Solution of Linear Homogeneous Differential Equations with Constant Coefficients on the Boundary Value Problem (in Chinese). Sichuan Ordnance Journal, 2010,31(4): 126-129.
 
[7]  Huang Rongjun, Li Shunchu, Xu Dongxu. Similar Constructive Method of Solution to Boundary Value of First Weber Equation (in Chinese). Journal of Mianyang Normal University, 2012, 31(11):1-5(-15).
 
[8]  Li Shunchu, Liao Zhijian. Constructing the Solution of Boundary Value Problem of the Differential Equation with its an Arbitrary Non-trivial Solution (in Chinese). Journal of Sichuan University (Natural Science Edition), 2012, 49(6):1209-1213.
 
[9]  LI Shun-chu. Preliminary Exploration and Prospects of the Similar Structure of Solutions of Differential Equations (in Chinese). Journal of Xihua University (Natural Science Edition), 2010,29(2):223-226(to238).
 
[10]  Tian Jidong, Li Shunchu. The Formal Similarity of Solutions in the Laplace Space on the Class of Quasilinear Partial Differential Equation. MATHEMATICAL THEORY AND APPLICATIONS, 2004, 24(2):66-73.
 
[11]  Jia Minhui, LI Shun-chu. The Formal Similarity of Solutions in the Laplace Space on the Class of Fluid Flow Differential Equation. Journal of Electronic Science and Technology of China, 2005,3(2):172-174.
 
[12]  SU Jian-peng, LI Shun-chu, LI Cheng-jie. The Similar of Solutions in the Laplace Space of Composite Parabolic Partial Differential Equation. Journal of Zaozhuang University, 2009,26(2):6-11.
 
[13]  LI Shun-chu. The Formal Similarity of Solutions in the Laplace Space on the Class of Partial Differential Equation System (in English). Journal of Xihua University (Natural Science Edition), 2007,26(4):83-86.
 
[14]  LI Shun-chu, ZHENG Peng-she, ZHANG Yu-fei. The Similar Structure of Pressure Distribution in the Homogenous Reservoir (in Chinese). Pure and Applied Mathematics, 2006,22(4):459-463.
 
[15]  XU wen-zhao, LI Shun-chu, ZHENG Peng-she. The Structure of the Solution of Pressure Distribution in the Fractal Homogenous Reservoir and Analytic Graph (in Chinese). Mathematics and its Applications. Beijing: Atomic Energy Publishing Company,2007: 541-544.
 
[16]  LI Shun-chu, ZHENG Peng-she, ZHANG Yu-fei. The Similar Structure of Pressure Distribution in the Composite Reservoir (in Chinese). Journal of Mathematics in Practice and Theory, 2008,38(3):23-28.
 
[17]  LI Shun-chu, ZHENG Peng-she, ZHANG Yu-fei. Similar structure of pressure distribution in the multilayer reservoir (in Chinese). Applied Mathematics A Journal of Chinese Universities, 2009,24(2):234-238.
 
[18]  LI Shun-chu, ZHANG Jian-jun. Similar Structure of Pressure Distribution in the Fractal Dual Porosity Reservoir (in Chinese). Journal of Xihua University (Natural Science Edition), 2006,25(1):40-43.
 
[19]  Xu changxue, Li Shunchu, Zhu Weibing, et al. The Similar Structure of Pressure Distribution in the Dual Porosity Reservoir (in Chinese). Drilling & Production Technology, 2006,29(4):28-30.
 
[20]  Xu changxue, Li Shunchu, Zhu Weibing. The Similar Structure of Pressure Distribution in the Fractal Composite Reservoir (in Chinese). Drilling & Production Technology,2006,29(5):39-42.
 
[21]  Zheng Pengshe, Li Shunchu, Zhang Yufei. The Formal Similarity of Solutions on the Class of Ordinary Differential Equation System (in Chinese)[J]. Journal of Jilin University (Information Science Edition), 2005,23(8):56-60.
 
[22]  Zhu Weibing, Li Shunchu, Xu changxue. The Similar Structure of Pressure Distribution in the Fractal Multilayer Reservoir (in Chinese). Drilling & Production Technology,2008,31(3):67-69(-72).
 
[23]  ZHENG Peng-she, LI Shun-chu, XU wen-zhao. WELL ANALYSIS METHOD BASED ON THE SIMILAR STRUCTURE OF PRESSURE DISTRIBUTION IN THE COMPOSITE RESERVOIR (in Chinese). Drilling & Production Technology,2007,30(3): 49-50(-62).
 
[24]  Xu Li, Li Shunchu, Wang Junchao. Similar Structure of the Solutions to Radial-Spherical Seepage Problem Considering Quadratic Gradient Effect (in Chinese). Journal of Chongqing Technology and Business University (Natural Science Edition), 2011, 28(6):585-589.
 
[25]  Li Wei, Li Xiaoping, Li Shunchu, Li Quanyong. Similar Structure of the Solutions of Mathematical Model for the Nonlinear Flow of Fractal Commingled Oil Reservoirs (in Chinese). Petroleum Geology & Oilfield Development in Daqing, 2012, 31(6):79-83.
 
[26]  LI Quanyong, LI Shunchu, LI Wei, WANG Junchao. Study of the Nonlinear Fluid Flow Modle in Dual-porosity Media Reservoir Based on Similar Structure. CHINESE JOURNAL OF ENGINEERING MATHEMATICS, 2013, 30(1):123-130.
 
[27]  Liu Shishi, Liu Shida. Special Function. Beijing: China Meteorological Press, 2002.