The Constructive Method And Its Application Of The Of Solutions To The Boundary Value Problem For Second-order Linear Homogeneous Differential Equation

The impacts of each parts of the BVP (the equation and boundary conditions) on thestructure of its solutions are analyzed for two non-homogeneous boundaries of thesecond-order homogeneous linear differential equation in this paper, which base on the theoryof the solutions to the similar structure. A new method to solve such problems is presentedwhich is defined as similar constructive method and the detailed examples and generalizationfor this method are given. The main contents are as follows:Firstly, two non-homogeneous boundaries of the second-order homogeneous lineardifferential equation are transformed into two boundary value problems which have only onenon-homogeneous boundary condition. Secondly, the kernel function is generated by thefunction of guide and the coefficients of boundary value conditions based on constructing thefunction of guide and the generating function of solutions, and the kernel function and thecoefficients of non-homogeneous boundary value conditions are assembled to obtain thesolution to the boundary value problem which have only one non-homogeneous boundarycondition. Then, the similar structures of the solution to the boundary value problem for twonon-homogeneous boundary conditions are obtained by superposition principle, and thesimilar construction method for solving such problems is presented. On the basis of this, thesimilar construction method is used to solve the hydrocarbon bearing pool percolation modeland some mathematical problems, then discussed and analyzed by the specific examples.Finally, the similar structure of the solution to the second-order homogeneous lineardifferential equation is promoted to solve the boundary value problem of the second-order andhigher-order homogeneous linear differential equation.The structure method can avoid the complex calculations and proof and simplify thesolution process so that it could make the solving steps clear. The similar structure methodsmake good effect on the analysis software solution, so it further enrich and perfect the similarstructure theory.