发展方程的计算稳定性问题

一、演变过程方程及差分格式 在数值天气预报中以及求解非定常流体运动时,必须设计计算稳定的格式,所以关于计算稳定性问题的理论研究是很有意义的.在这一类问题中,所要求解的问题大都可以

ON THE COMPUTATIONAL STABILITY OF EVOLUTION EQUATIONS

Many problems in weather forecast, non-steady fluid mechancis and applied physicscan be reduced to "evolution equations". In this paper, the computational stability ofthe evolution equations is discussed with formal generalized operator equations. It isshown that computational stability is closely related to the conservation property ofenergy or non-negativity of difference operator; Some special examples of computation-al instability are given for the schemes not satisfying energy conservation ("genera-lized energy conservation" included) and the non-negative operators.