对流方程的一族高精度恒稳格式

A Group of Steady Schemes with High Accuracy for Solving Convective Equation

为求解对流方程 ut=aux 构造一族新的含 3参数 3层隐式差分格式 (在特殊情况下是 2层 ) ,其截断误差至少可达 O[( Δt) 2 +( Δx) 4].在条件 α1=α3,|α2 |≤ 2 |α1|或 α1≥ 0 ,α2 ≥ 0 ,α3≥ 0 ,α1>α3,α1+α2 +α3=1,α2 ≤ 1/ 2之下 ,绝对稳定 .特别地 ,当参数 α1=α2 ,α3=0时得到一个两层恒稳的差分格式 .所有这些格式都可用追赶法求解 ,它包含对流方程的已有文献中的隐式高精度恒稳格式 .

For solving convective equation u t=au x , a new group of implicit different schemes containing three parameters are constructed. They are three layers in general and two layers in special case. Their truncation error wile reach O [(Δ t ) 2+(Δ x ) 4] at least. Under the conditions of α 1=α 3,｜α 2｜≤2｜α 1｜ or α 1≥0, α 2≥0, α 3≥0,α 1>α 3, α 1+α 2+α 3=1,α 2≤12 ,they are absolutely stable. Particalarly, a two layer steady difference scheme can be obtained in case parameter α 1=α 2,α 3=0 . All these schemes, with all steady ones with high accaracy in literatures included, can be solved by applying double sweeping method.