Block-Centered Difference Method For Viscoelasticity Equation And Rlw Equation

In this paper, we use the block-centered finite difference method to solve linear equa-tion of the viscoelasticity equation and regularized long wave equation initial boundary value problem, respectively. We not only get the approximate solution and the approxi-mate solution of the first order derivative of the approximate value, but also can obtain the discrete L2-norm errors and the super convergence of the approximate solution of the first order derivative of the approximate value.First of all, there is an overview of the research background and development status of the problem, and simply introduce the work we do and the basic theory of knowledge in this paper.Moreover, through introducing a derivative variable, we structure the block centered difference format in an isometric mesh for the initial boundary value problem of the vis-coelasticity equation and regularized long wave equation. Then we do error estimation, analyse and prove the convergence and stability. In the end, the results show the correct-ness of the theoretical analysis from giving the corresponding numerical examples, and also show that the method is feasible and effective.Finally, the summary and the prospects of equation were given.