若干差分格式非线性计算稳定性研究的新进展

New Advances in Research on Some Difference Schemes in Nonlinear Computational Stability

考察了有代表性的３类发展方程，指出其对应的差分格式是否出现非线性计算不稳定，与原微分方程解的性质密切相关。进一步讨论了带周期边条件的守恒型差分格式的非线性计算稳定性问题，总结了克服非线性不稳定的有效措施。以非线性平流方程为例，着重分析了带非周期边条件的非守恒差分格式的非线性计算稳定性问题，给出了判别其计算稳定性的“综合分析判别法”。

Three types of representative evolution equations are analyzed. The close relationship between the nonlinear computational stability or instability of their corresponding difference equations and the properties of their solution are revealed. Nonlinear computational instability problem of conservative difference equations with periodic boundary condition is further discussed, and some effective ways to avoid nonlinear computational instability are included. Nonlinear computational instability of non-conservative difference equation with aperiodic boundary condition is focused on by using nonlinear advection equations as examples, and the 'synthetical analysis method' is given to judge their computational stability.