【摘要】 为建立一维抛物型方程适合在并行机上计算的差分方法,构造截断误差达到O(Δt3+Δx4)的一个含参数β1高精度三层隐式差分格式,其稳定性条件是1β≥r/2(r=aΔt/Δx2),然后以此隐式差分格式为基础,设计出一种交替分组显式迭代(AGE I)方法,并证明了交替分组显式迭代过程的收敛性,由于AGE I方法的计算过程是显式的,所以非常适合并行计算.数值算例表明具有很高的精确度和良好的实用性.更多还原

【Abstract】 In order to propose a difference method suitable to parallel computer,a family of single parameter and implicit difference schemes for solving one-dimensional parabolic differential equations were presented in this paper.The local truncation error was O(Δt3+Δx4),the stable condition of schemes was β1≥r/2(r=aΔt/Δx2),then an alternating group explicit iterative(AGEI) method was proposed and convergence of the iterative process was proved.Because the whole calculation process is explicit,the AGEI method is very suitable to parallel arithmetic.Numerical example shows that the AGEI method has high accuracy and good practicability.更多还原