解高阶抛物型方程的一族隐式差分格式

A Family of Implicit Difference Schemes for Solving the Parabolic Equation of Higher Order

对高阶抛物型方程t=(-1)m+1x2m(m为正整数),构造一族含双参数的三层隐式差分格式·在特殊情况下,当参数α=21,β=0时得到一个双层格式·这些格式的截断误差阶均为O((Δt)2+(Δx)4).证明当m=1,2,3时,这些格式对任意非负参数α≥0,β≥0都是绝对稳定的·数值例子表明,所得格式是有效的,其理论分析是正确的·

For solving the parabolic equation of higher order [SX(] u[] t[SX)]=(-1) m+1 [SX(] 2m u[] x 2m [SX)] (where m is a positive integer), a family of three-layered implicit difference schemes containing biparameters are constructed. In a special case, a two-layer scheme is obtained when parameter α=[SX(]1[]2[SX)], β=0. The order of the truncation error of all these schemes is O ((Δ t ) 2+(Δ x ) 4). These schemes are proved to be absolutely stable for arbitrarily chosen non-negative parameter α≥0, β ≥0 when m =1,2,3. As shown by numerical examples, these schemes are effective and the theoretical analysis is correct.