多维空间不均匀网格差分格式的稳定性判别法

Criterion on Stability of the Difference Schemes with Uneven Mesh Spacing in Multiple Dimensional Spaces

讨论了多维空间中关于一个坐标面的正负两边具有不均匀网格的差分格式的稳定性,依据Michelson理论,应用付氏分析法把其它坐标的对偶变数作为参数,因此,问题化为单个变量情形的不均匀网格差分格式的稳定性问题,因此可以应用Kreiss稳定性判别法来处理这个问题。

A finite difference approximation to the Cauchy problem for a first orderiy hyperbolic partial differential equation with different mesh specings in different portions of the domain is considered. By reformulating the problem as a difference approximation to an initial boundary value problem, the stable theory of D. Michelson and H. O. Kreiss is used to analyze the L2, stability of the schemes.