Similarity Construction Of Solutions For Discontinuous Differential Equation Boundary Value Problems

Based on the similarity construction theory of boundary value problems of differential equations,this thesis studies and constructs the solution of boundary value problems of discontinuous differential equations with multiple transfer conditions,and applies the similarity construction method to the solution of boundary value problems of discontinuous Kummer equations.Firstly,the solution function is introduced and the similar kernel function of the boundary value problem of discontinuous differential equation is constructed.Then,through strict theoretical derivation,the solution of the boundary value problem of discontinuous equation with a transfer condition is obtained.The validity of the similar construction method and the dependence of the solution on the boundary conditions are demonstrated by examples.Secondly,the similarity construction method is extended to solve the boundary value problem of discontinuous differential equations with multiple transfer conditions.Finally,the solution of the discontinuous Kummer equation boundary value problem is obtained by the similarity construction method,the results show that this method can effectively solve such problems.The main work of this thesis is as follows:In chapter 1,introduces the research significance and research status of the similar construction method for the boundary value problem of secondorder differential equations,and briefly expounds the related theories of the boundary value problem of differential equations.In chapter 2,based on the boundary value problem of discontinuous equations with special transfer conditions,the form of solutions to the boundary value problem of discontinuous differential equations with general transfer conditions is studied,and the similar structural solutions of the problem are constructed.In chapter 3,by solving the boundary value problem of differential equations with one transfer condition,the solution of the boundary value problem of differential equations with multiple transfer conditions is studied,and the solution of the boundary value problem is constructed and proved.In chapter 4,we use the similarity construction method to solve the boundary value problem of discontinuous Kummer equation with general transfer conditions,and study the relationship between the form of the solution of the boundary value problem,the coefficients of the transfer conditions and the coefficients of the boundary conditions.In chapter 5,summarizes and prospects this thesis,and looks forward to subsequent related work.