Algrithm Study Of Nonlinear Differential Equation With Nonlinear Boundary Conditions

Fourth-order differential equations with nonlinear boundary conditions because of its important physical background has been attracting the attention of many academics,and abundant research results have been achieved.In recent years,more and more research on elastic beam equations in public view,now its main focus on examination of equation solution and the existence of positive solutions and the diversity and so on,by applying the Lelyschede continuation method,extension method of topological degree theory,in cone fixed point theorem,in critical point theory or upper and lower solution method.Fourth-order differential equations with nonlinear terms can describe the deformation of static beam,and different boundary value conditions correspond to different support modes.In this paper,we discuss a class of fourth order differential equations with nonlinear boundary conditions,using the parameters of the ? replace nonlinear term of the boundary value conditions,construct a function u(x)contains parameters and reproducing kernel space W52[0,1].The solution of equation with a parameter through the Fourier series,given the initial function u0(x)and iterates the solution of the equation in turn and the solution of the problem whose parameters can be obtained.In this paper,the error estimation and convergence analysis of the regenerative kernel method for solving nonlinear boundary value problems are given,and some numerical examples are given to prove the applicability of the method.