非线性发展方程的非守恒格式的计算稳定性问题

The Computational Stability of Nonconservative Schemes of Nonlinear Evolution Equations

针对非线性发展方程的非守恒格式 ,以一维浅水波方程为例 ,对非守恒格式的计算稳定性进行了研究分析 ,探讨了非线性发展方程的非守恒格式与初值的关系。理论分析和数值试验表明 ,在格式结构已经确定的情况下 ,非守恒格式的计算稳定性主要由初值的形式所决定。

For the nonconservative schemes of nonlinear evolution equations, taking one dimensional shallow water wave equation as an example, the necessary conditions of computational stability are given. Based on the numerical tests, the relationship among the nonlinear computational stability, the construction of difference schemes, and the form of initial values is further discussed. It is proved through theoretical analysis and numerical tests that the computational stability of nonconservative schemes is not only dependent on the structure of scheme, but also on the form of initial values and their partial derivatives.