eng Science and Education Publishing American Journal of Applied Mathematics and Statistics 2328-7292 2013-09-25 1 1 76 82 10.12691/ajams-1-4-5 AJAMS2013145 article Dong Xiaoxu dongxiaoxu1028@163.com 1 Li Shunchu 1 Gui Dongdong 2 Pu Jun 2 Li Huichun 3 School of Mathematics and Computer Engineering, Xihua University, Chengdu, China Beijing Dongrunke Petroleum Technology Co., Ltd., Beijing, China Geological Research Department of the Fourth Oil Production Plant of DaGang Oilfield Company, Tianjin, China 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. http://pubs.sciepub.com/ajams/1/4/5/ajams-1-4-5.pdf boundary value problem composite Weber system similar constructing method similar kernel function function of guide solution