The Analytical Solutions And The Finite Difference Numerical Solutions Of Telegraph Equations With Nonlocal Boundary Conditions

Telegraph equation is one of the important mathematic-physics equations.It has been applied in many different fields,such as the propagation of electric signals,the propagation of dispersed waves,mechanical systems,vibration systems and so on,and the hyperbolic equation is a special form of telegraph equation.In this paper,the analytical solutions and the finite difference numerical solutions of telegraph equations with nonlocal boundary conditions will be studied.In this paper,Firstly,a brief introduction to the research background of nonlocal problems and telegraph equations is given.Secondly,the related concepts and basic properties of self-conjugate boundary conditions are given,and self-conjugate StrumLiouville eigenvalue problems are discussed.Thirdly,the analytical solutions of three types of nonlocal telegraph equations are discussed by using the method of variables separation.Then,the discrete difference scheme of a type of telegraph equations with nonlocal boundary conditions is given,and the local truncation error of the discrete difference scheme is obtained by using Taylor formula.The stability of the main format is analyzed by using the Fourier method,and the convergence of the difference format is proved by the method of discrete Fourier transform.Finally,the numerical experiments and the results of the analysis of three nonlocal telegraph equations are given,which verify the correctness of the numerical theory.