一种判定非线性平流方程差分格式计算稳定性的新方法

A New Method for Judging the Computational Stability of the Difference Schemes of the Nonlinear Advection Equation

非线性计算稳定性是计算数学、计算物理等学科中的一个重要问题。针对非线性发展方程的非周期边界条件 ,本文以一维非线性平流方程为模型 ,给出一个较普遍的差分格式 (以往若干常见平流格式均为其特例 !) ,给出了一种判定差分格式计算稳定性的新方法。数值试验证明是有效的和实用的 ,得到的稳定性判据的确是保证差分格式计算稳定的必要条件。

The stability of the nonlinear computation is important to the numerical mathematics and the computing physics.For the difference schemes of nonlinear evolution equations with aperiodic boundary conditions,taking one\|dimensional nonlinear advection as an example, a new and relatively general difference scheme is given.A new method for judging the computational stability is given.It is proved that the method is a practical and effective one by several numerical examples.The stability criteria obtained by this method really are the necessary conditions of computational stability.