Numerical Methods For Fourth-order Integro-differential Equations

There are many integro-differential equations in the process of research in mathematical and hysical problems. The research of the solutions of the equations has become an important work scientific and technological workers. In most case, it is difficult to find the analytical solution the equations, or even impossible. Therefore, the investigation of the numerical method is very neaningful.In this thesis, firstly, we consider the numerical solution of the four-order integral-differential quations of the suspension bridge model. The collocation method are used to find the approxi-nation solution of Bernoulli polynomials and the error estimation is given. Through the residual unction we obtained the improved Bernoulli polynomials approximation solution. In addition, sing the variational iteration method, we also gives the numerical scheme for the four-order ntegro-differential equation. Numerical examples are implemented to illustrates the feasibility of he algorithm.Secondly, based on the τ method, we give the Bernoulli polynomials approximation for an-ther class of fourth-order integro-differential equations. The error estimation of the method is resented. The numerical examples are also implemented. Comparing with existing numerical methods, we get a higher accuracy scheme.