对流方程一族新的三层双参数高精度格式

A New Family of Three-Layer and Bi-Parametric Difference Schemes with High Accuracy for Solving Convection Equation

对对流方程 ut=aux(其中 a为常数 ) ,构造一族新的含双参数高精度的三层差分格式 .当参数α=12 ,β=0时 ,得到一个双层格式 .这些格式对任意选取的非负参数都是绝对稳定的 ,其局部截断误差阶为 O((Δt) 2 +(Δt) 2 (Δx) 2 +(Δx) 6) .数值试验表明 ,所建立的差分格式是有效的 ,理论分析是正确的 .

For solving convection equation u t=au x , where a is a constant, a new family of three-layer and biparametric difference schemes with high accuracy are constructed; and a double layer scheme will be obtained in case α =12 and β =0. All these schemes are absolutely stable for non negative parameters chosen arbitrarily with the local truncation error of O((Δ t ) 2+(Δt) 2(Δ x ) 2+(Δ x ) 6). As indicated by numerical experimentation, the difference schemes so established are effective and the theoretical analysis of them is correct.