M.K.D.V方程高阶全离散Galerkin有限元格式

On Some High Order Accurate Full Discrete Galerkin Method for the M.K.D.V Equation

本文用对角隐式Runge-Kutta方法(D.I.R.K),对M.K.D.V.方程在时间方向离散,采用增加扰动项的办法,得到了L^2模意义下时间方向具有三阶精度的格式。数值实例表明,其精度比无拢动项及C-N格式好。还证明了收敛性和稳定性,用Newton迭代法求解非线性方程组,并证明选取适当的初始值,Newton迭代仅需一步完成。

In this paper, we use the Diagonally Implicit Runge-Kutta method and Pertubing small term for the M. K. D. V. equation Discretion in time stepping on L^2-Norm. We have the scheme of a third order of accuracy in time stepping and prove the convergence and stability of this scheme. We also prove these non-linear system of equations are solved by Newton's method. Provided the initial iterates are chosen in a specific we show that only one Newton iteration per system is needed to preserve the stability of order of accuracy of the scheme, finally, we also give a numerical example.