Science and Education Publishing American Journal of Applied Mathematics and Statistics 2328-7292 1 1 2013 09 25 Similar Constructing Method for Solving the Boundary Value Problem of the Composite First Weber System 76 82 EN Dong Xiaoxu School of Mathematics and Computer Engineering, Xihua University, Chengdu, China Li Shunchu Gui Dongdong Pu Jun Li Huichun AJAMS2013145 10.12691/ajams-1-4-5 2013 07 21 2013 08 16 2013 09 25 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.