高阶发展方程的两类显式格式的稳定性分析

Stability Analysis of Two Classes of Explicit DifferenceSchemes for High-Order Evolution Equations

对高阶发展方程给出了两类带参数α的三层显式差分格式，其截断误差均为Ｏ（τ＋ｈ）．稳定性分析指出：当ｋ为偶数时，它们无条件不稳定；当ｋ为奇数时，稳定条件为｜Ｒ｜≤ｆ（ｋ，α）是α（０≤α≤１０）的上升函数，但为ｋ的下降函数．例如，当ｋ＝１时，ｆ（１，３）＝０．９８７１２３，ｆ（１，１０）＝２．１５０６９０；当ｋ＝３时，ｆ（３，３）＝０．１０９１５３，ｆ（３，１０）＝０．３１９０３６；当ｋ≤９（奇数）时，它们较大地改进了同类格式的稳定性条件｜Ｒ｜≤１／２２ｋ．

Two classes of three-level explicit difference schemes with parameter a and the same truncation error O(r+h),are given here for the evolution equations of high-order As shown by stabilityanalysis, while k is an even number, they are unconditionally unstable; while k is an odd number, they havethe stability condition |R|≤f(k,α) which is the increasing function of α(0≤α≤10) and the decreasing function of k.They are richly exemplified.