多维空间双曲型方程差分逼近的全能耦合稳定联接格式

The Universal Matching Stable Connected Scheme for the Multidimensional Scalar Hyperbolic Equation

在多维情形下提出一种全能耦合稳定联接格式，只要相邻区域Ｄ（ａ）ｉ，Ｄ（ａ）ｉ＋１的格式Ｒ（ａ）ｉＲ（ａ）ｉ＋１分别为柯西稳定，并在中介面附近的某区域Ｄ（ａ）ｉ，ｉ＋１中应用全能耦合稳定格式Ｑ（ａ）ｉ，ｉ＋１，则整体格式Ｒ（ａ）ｉ，Ｑ（ａ）ｉ，ｉ＋１，Ｒ（ａ）ｉ＋１必为区域套网格耦合稳定．

In the multidimensional space, if any two schemes R(a)i,R(a)i+1 between two consecutive regions D(a)i,D(a)i+1 are Cauchy stable respectively and are interpolated by an universal matching stable connected scheme Q(a)i,i+1,then the region nesting grid difference approximations R(a)i,Q(a)i,i+1,R(a)i+1 in the whole for the multidimensional scalar hyperbolic equation are al ways matching stable.