Block-centered Difference Methods For Wave Equation And Two-dimensional Viscoelastic Equation

Nonlinear wave equation and two-dimensional viscoelastic equation are two impor-tant classes evolution equations and widely applied to physics,economics,natural science and many other areas.So many scholars have done a lot of researchs for the two equation-s.But they only get the approximate solution of the equations.In this paper, we discussed the two-dimensional viscoelastic equation and nonlinear wave equation with the block center finite difference method for all grids. We not only obtain the approximate solu-tion and the approximate solution of the first order derivative of the approximate value,but also can find out the discrete L2-norm errors of the approximate solution and super convergence estimateits of the approximate solution of the first order derivative of the solution.First of all, we simply introduce the research background of the problem discussed in the paper, and briefly introduce the basic theory of knowledge.Moreover, for the two-dimensional viscoelastic equation in the bounded domain, we get the approximate solution and the approximate solution of the first order derivative of solution for all nonuniform grids with the block center finite difference method. In theory,we get the discrete L2-norm errors of the approximate solution and super convergence estimateits of the approximate solution of the first order derivative of the solution. It is import that we get higher precision in time. Similarly, when we use the block center finite difference method to study the nonlinear wave equation in the bounded domain, we also get the approximate solution and the approximate solution of the first order derivative of solution for all uniform grids. We can also get the discrete L2-norm errors of the approximate solution and super convergence estimateits of the approximate solution of the first order derivative of the solution in theory.Finally, the summary the next studying problem of equation were given.