抛物型方程的一种高阶并行差分格式  

A high-order parallel difference scheme for a parabolic equation

作　　者：孙凯[1] 王文洽[1] 

机构地区：[1]山东大学数学学院,山东济南250100

出　　处：《山东大学学报（理学版）》2009年第2期39-44,共6页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(10671113)

摘　　要：构造了求解抛物方程的高阶并行差分格式。首先,通过前三个时间层内界点的值及四阶紧致格式并行计算子区域的值,然后再用区域边界点显式计算内界点的值,并证明算法的稳定性条件至少为(2^(1/2))/3+1/6,收敛精度为四阶。最后用数值算例验证算法的稳定性及收敛性,数值结果表明此算法具有比其他算法更好的精度。A high order parallel finite difference algorithm of a parabolic equation was presented. First, the values of the previous three levels at the interface points were combined with the compact scheme to solve the values of sub-domains in parallel, then the values at the interface points were computed by the compact scheme. The stability bound of the procedure was derived to be at least√2/3＋1/6, and the convergence rate was proved to be of order four. Numerical examples show that this method has much better accuracy than other methods.

关 键 词：抛物型方程 并行差分格式 四阶精度 区域分解算法 

分 类 号：O241[理学—计算数学]