A Comparative Analysis of Computational Stability for Linear and Non-Linear Evolution Equations
线性与非线性发展方程计算稳定性的比较分析

For several difference schemes of linear and non-linear evolution equations, taking the one-dimensional linear and non-linear advection equations as examples, a comparative analysis for computational stability is carried out and the relationship between non-linear computational stability, the construction of difference schemes, and the form of initial values is discussed. It is proved through comparative analysis and numerical experiment that the computational stability of the difference schemes of the non-linear evolution equation are absolutely different from that of the linear evolution equation.