抛物型方程的一族双参数高精度恒稳格式

A Family of High Accurate and Steady Difference Schemes with Double Parameters for Solving Parabolic Equations

对抛物型方程 ,构造一族含双参数的三层高精度隐式差分格式 .在特殊情况下 ,当参数α=12 和β=0时 ,得到一个两层格式 .同时 ,证明该族格式对任意非负参数都是绝对稳定的 ,并且其截断误差阶为 O((Δ t) 2 + (Δx) 6) .数值例子表明 ,该族格式是有效的 ,且理论分析与实际计算相吻合 .

A family of three layer implicit difference schemes of high accuracy with double parameters are constructed for solving parabolic equations. Under special circumstance when the parameter α =12 and β =0, a two layer difference scheme is obtained. These schemes are proved to be absolutely stable for arbitrary non negative parameter, and their truncation error is in the order of O ((Δ t ) 2+(Δ x ) 6). As showm by numerical example, the family of difference Schemes are effective and theoretical analysis of them coincides with practical calculation of them.