解四阶抛物型方程的三层高精度显格式

Explicit Difference Scheme of 3 Level High Accuracy for Solving Four Order Parabolic Equation

对四阶抛物型方程构造一族新的含参数三层显式差分格式 .它包含了DuFort -Frankel型格式 .适当选取参数时 ,可得到一个新的高精度显格式 ,其截断误差达到O[(△t) 2 +(△x) 6],其稳定性条件为γ =△t(△x) 4 ≤ 3136 0 ,优于文 [1]的稳定条件 .当选取γ =12 5 2 时 ,其截断误差高达O[(△t) 2 + (△x) 8],数值例子表明该格式是有效的 .

For solving four-order parabolic equation,a new group of explicit difference scheme contains Du Fort-Frankel difference schemes.When parameters are properly chosen,we obtain an explicit difference scheme of high accuracy.its truncation error reach O((△t) 2+(△x) 6) .It is stable under the condition of γ=△t(△x) 4≤31360 ,tstable condition is better than that of explicit scheme in .When γ=1252 ,its truncation error can reach O[(△t) 2+(△x) 8] .a numerical example shows that these schemes is effectives.