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

Dong Xiaoxu^1, , 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

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

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