【摘要】 以最典型的非线性色散方程 Kd V方程为模型 ,着重讨论了两类较普遍的三时间层和二时间层差分格式的计算稳定性问题 ,给出了一种判定差分格式计算稳定性的新方法 ,数值试验证明是实用和有效的 ,得到的稳定性判据的确是保证差分格式计算的必要条件。Kd V方程不会产生非线性计算不稳定 ,产生的只是线性计算不稳定 ,可以用缩短时间步长来克服 ;计算试验证实三时间层格式容易产生计算不稳定 ,二时间层格式易于稳定 ,并且发现参数取 2 /3时 ,计算结果最好。更多还原

【Abstract】 In this paper, the nonlinear dispersive equation is KdV equation adopted as model. The computational stability of two kinds of general three time level schemes and two time level schemes are analyzed, a new method for judging the computational stability is given. It is proved to be practical and effective though several numerical examples. The stability criteria obtained by this method are really the necessary conditions of computational stability. KdV equation does not made nonlinear computational instability,it only produces line computational instability, but line computational instability can be overcome by reducing time steps. By means of qualitative analysis and numerical experiments, it is shown that computational instability is prone to occur for three time level schemes, but two time level schemes made computational stability easy,and the numerical results is best when parameter equal 2/3.更多还原