抛物型方程的一族高精度恒稳格式  

A Group of Steady Difference Schemes wth High Accuracy for Solving Parabolic Equation

作　　者：黄浪扬[1] 曾文平[1] 

机构地区：[1]华侨大学管理信息科学系,泉州362011

出　　处：《华侨大学学报（自然科学版）》2000年第2期124-128,共5页Journal of Huaqiao University(Natural Science)

摘　　要：对二阶抛物型方程 ut=uxx,构造了一族新的三层隐式差分格式 (在特殊情况下是两层 ) .它们含有非负参数α1 ,α2 和α3 ,其截断误差至少可达 O((Δt) 2 +(Δx) 4 ) .对三层格式 ,在条件α1 ≥α2 ≥0 ,α2 ≤ 12 及α1 +α2 +α3 =1之下绝对稳定 .特别地 ,在条件α1 =0 ,α2 =α3 或α1 =α2 ,α3 =0之下成为两层不含参数的隐式格式 ,且也是绝对稳定的 .这些格式均可用追赶法求解 .在该格式中 ,选取适当的参数 ,可得抛物型方程初边值差分格式中的高精度格式 .A new group of three layer implicit differemce schemes, which can be two layer in special case, are constructed for solving second order parabolic equation where u t=u xx . They contain non negative parameter α 1, α 2 and α 3, with truncation error up to O ((Δ t ) 2+(Δ x ) 4) at least. Under the conditions of α 1≥ α 3≥0, α 2≤12 and α 1+ α 2+ α 3=1, these three layer schemes are absolutely stable. Under the conditions of α 1=0, α 2= α 3 or α 1= α 2, α 3=0 as a special case, they become two layer but remain absolutely stable. All these schemes can be solved by double sweeping method. By choosing proper parameter, highly accurate schemes in difference schemes with initial boundary value can be obtained for solving parabolic equation.

关 键 词：二阶抛物型方程 绝对稳定 稳式差分格式 

分 类 号：O175.26[理学—数学]