The Construction Method And Applications Of The Boundary Value Problem Of Three-Area Composite Differential Equation

This paper studies the boundary value problem of three-area composite second-order linear homogeneous differential equation. On the basis of the theory of similar structure of solution of the boundary value problem of differential equation, a new method for solving the class of boundary value problems of differential equation-similar constructing method is obtained. The concrete research contents of this paper are as follows:Firstly, this paper obtains the similar structure of solution of the boundary value problem of three-area composite second-order linear homogeneous differential equation in virtue of introducing functions of guide solution and constructing similar kernel functions. After rigorous mathematical derivation and analysis, a new method for the class of boundary value problems of three-area composite differential equation-similar constructing method is obtained. Then this paper sums up detailed solving steps of the new method and gives the corresponding flowchart of algorithm of the boundary value problem. Secondly, this paper uses the method to solve the boundary value problem of three-area composite Bessel equation, the boundary value problem of three-area composite modified Bessel equation and the seepage flow model of three-area composite reservoir. Finally, the similar structure solution of the boundary value problem of n areas composite second-order linear homogeneous differential equation is obtained by extending the similar structure solution of the boundary value problem of three-area composite second-order linear homogeneous differential equation. Then the similar structure solution of the boundary value problem of n areas composite differential equation is proved by using second mathematical induction.