CAJ | 학술논문

本文中提出了求解Burger’s方程的两水平方法。新方法只需在粗网格上求解一个网格步长为H的非线性问题，在细网格上求解一个网格步长为h的线性问题。新格式是隐式无条件稳定的，并且能够得到与单水平解相同的收敛阶。由于单水平方法在细网格上求解一个大型非线性问题，所以我们的方法可以节省大量的计算时间。
본문중제출료구해Burger’s방정적량수평방법。신방법지수재조망격상구해일개망격보장위H적비선성문제，재세망격상구해일개망격보장위h적선성문제。신격식시은식무조건은정적，병차능구득도여단수평해상동적수렴계。유우단수평방법재세망격상구해일개대형비선성문제，소이아문적방법가이절성대량적계산시간。
In this paper, a two-level finite difference scheme is presented for the numerical approximation of Burger’s equation. The full nonlinear problem is solved on a coarse grid of size H , and a linear problem is solved on a fine mesh with mesh size h. The new difference scheme, which is the implicit one with unconditional stability and easy computation. The method we study provides an approximate solution with nearly the same error as the usual one-level solution, which involves solving one large nonlinear problem on a fine mesh with mesh size h. Hence, our method is capable of significantly saving computational time.