摘要
建立了解三维抛物型方程的一族含参数的绝对稳定的高精度差分格式．李荣华等的结果可以看作两层差分格式的特例．进而，在特殊情况（θ＝０，ｒ＝１／６）下，我们得到显式差分格式．我们证明了这些格式对任意选取的参数θ≤１／３都是绝对稳定的且其截断误差阶为０（Δｔ）２＋Δｔ（Δｘ）２＋（Δｘ）４）＝０（（Δｔ）２）．
For solving three-dimensional parabolic equation, the author establishes a family of absolutely stable and high accurate difference schemes with a parameter.The results of reference may be regarded as special cases of two-level difference scheme. Moreover, an explicit difference scheme is obtained under the special case of (θ=0, r= 1/6). The schemes are proved to be absolutely stable for θ≤1/3, parameters chosen arbitrarily;and their truncation errors are in the order of 0((Δt)2 +Δt(Δx)2+ (Δt)4=0(Δt)2 ).
出处
《华侨大学学报（自然科学版）》
CAS
1994年第3期257-262,共6页
Journal of Huaqiao University(Natural Science)
关键词
差分格式
抛物型方程
三维
绝对稳定
difference schemes, parabolic equations, three-dimension, high accuracy,absolutely stable
