Similar Constructing Method for Solving the Boundary Value Problem of the Composite Thomson Equation

Abstract

Based on the theory of similar structure of solution of the boundary value problem of differential equation, this paper studies the solution of a class of boundary value problem of the composite Thomson equation, After analysis? it is indicate that the solution with a form of continued fraction product is obtained by introducing functions of guide solution, constructing similar kernel functions and assembling coefficients of the left non-homogeneous boundary condition, functions of guide solution and similar kernel functions in this paper. Then a new method is obtained for solving the composite boundary value problem——Similar Constructive Method. Furthermore, the function solution is clearly illustrated by the chart which is carried out by the corresponding program in MTLAB. Thus, the method is not only simple and effective for solving the complicated boundary value problem of differential equation, but also is a kind of innovation of ideological.