发展方程的非线性计算不稳定问题

进一步讨论了有关非线性不稳定的一些问题,其主要内容有： １．考察了有代表性的三类发展方程,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。 ２．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。 ３．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”。

Problems of nonlinear computational instability in evolution equations

Some problems of nonlinear computational instability are discussed in this article, which are shown as follows: 1) Three types of representative evolution equations are analyzed, and the close relationship between the nonlinear computational stability or instability in their corresponding difference equations and the properties of their solution is revealed. 2) The problem of nonlinear computational instability in conservative differencing equations with the periodic boundary condition is further discussed, and some effective ways to avoid nonlinear computational instability are proposed. 3) The problem of nonlinear computational instability in non-conservative difference equations with the aperiodic boundary condition is focused on by using nonlinear advection equations as examples, and "snynthetic analysis method"is given to judge their computational stability.