【摘要】 讨论含参数β的局部截断误差为O（τh+h²）的色散方程u_τ=au_xxx的三层（中间层含8个点）显格式,对稳定条件的计算作了严谨的数学论证,用三种不同于[2]的方法复出了最佳稳定条件|aτ/h³|≤4.0lll7,β₀=1.57084.大大大优于[3]中的条件|aτ/h³|≤3.1099.更多还原

【Abstract】 A class of threelevel explicit difference schemes with local truncation errors O(ch + A2) for the dispersive equation u, = auxxx is discussed in this paper, these schemes contain a parameter B and eight net points in the middle level. The computing process of stability condition for the schemes is explained strictly in theory. Applying three methods different from the numerical experiment method used in [2] to calaulate.the optimum stability condition,we obtain |R|< 4. 01117(B =1. 57084),which is much better than the conditioin |R| <3. 1099[3],and seems to be the best result among the eightpoint explicit schemes at present.更多还原