The Numerical Value Method And Theoretical Analysis For Nonlinear Wave Equation With Interior And Exterior Domain

The contents of this dissertation are divided into two chapters.In chapter one, we build two time difference discrete implicit schemes for a class of third-order nonlinear wave equation with interior domain. And by using reproducing kernel function,the approximate solution of each time layer is expressed to explicit integral form. Then by using the energy method,the convergence and stability of the schemes are proved.At last,we give some numerical results.In chapter two, the coupling equation of finite element and boundary integral methods is applied to a class of three-order nonlinear wave equation with exterior domain.Variable replacement is applied to reduce the order of the nonlinear equation ,changing into a nonlinear parabolic equation .Then we study the coupling approximate problem of the parabolic equation: mading a artificial boundary divide the unbounded domain into two regions-annular region and unbounded region.We study the nonlinear equation in annular region and the corresponding linear equation in unbouded region. And we give the stability analysis and error estimate.