Class of Alternating Group Method of Burgers’ Equation
-
摘要: 对于Burgers方程给出了一组新的Saul'yev型非对称差分格式，并用这些差分格式构造了求解非线性Burgers方程的交替分组四点方法．该算法把剖分节点分成若干组，在每组上构造能够独立求解的差分方程．因此算法具有并行本性，能直接在并行计算机上使用．文章还证明了所给算法线性绝对稳定．数值试验表明，该方法使用简便，稳定性好，有很好的精度．
-
关键词:
- Burgers方程 /
- Saul'yev型非对称格式 /
- 交替分组四点格式 /
- 线性绝对稳定 /
- 并行计算
Abstract: Some new Saul'yev type asymmetric difference schemes for Burgers'equation is given,by the use of the schemes,a kind of alternating group four points method for solving nonlinear Burgers' equation is constructed here.The basic idea of the method is that the grid points on the same time level is divided into a number of groups,the difference equations of each group can be solved independently,hence the method with intrinsic parallelism can be used directly on parallel computer.The method is unconditionally stable by analysis of linearization procedure.The numerical experiments show that the method has good stability and accuracy. -
[1] Evans D J,Abdullah A R B.Group explicit methods for parabolic equations[J].Internat J Computer Math,1983,14(1):73—105. doi: 10.1080/00207168308803377 [2] Evans D J.Alternating group explicit method for the diffusion equations[J].Appl Math Modelling,1985,9(3):201—206. doi: 10.1016/0307-904X(85)90008-3 [3] Evans D J,Abdullah A R B.A new explicit method for the diffusion-convection equation[J].Comput Math Appl,1985,11(1/3):145—154. doi: 10.1016/0898-1221(85)90143-9 [4] ZHANG Bao-lin,SU Xiu-min.Alternating block explicit-implicit method for two-dimensional diffusion equation[J].Internat J Computer Math,1991,38(3/4):241—255. doi: 10.1080/00207169108803972 [5] ZHANG Bao-lin,LI Wen-zhi.On alternating segment Crank-Nicolson scheme[J].Parallel Computing,1994,20(8):897—902. doi: 10.1016/0167-8191(94)90123-6 [6] Evans D J,Sahimi M S.The numerical solution of Burgers' equations by the alternating group explicit(AGE) method[J].Internat J Computer Math,1989,29(1):39—64. doi: 10.1080/00207168908803747 [7] Evans D J,Abdullah A R B.The group explicit method for the Burgers' equations[J].Computing,1984,32(3):239—252. doi: 10.1007/BF02243575 [8] 陈金甫，张宝琳，徐涛.二维Burgers方程的AGE方法与并行计算[J].计算物理，1998，15(2)：225—233. [9] 金承日，刘家琦.Burgers方程的交替分组显示迭代方法[J].计算物理，1998，15(5):607—613. [10] 王子丁，陆金甫，肖世江.Burgers方程的一个分组显式格式[J].计算物理，1993，10(4):479—487. [11] Kellogg R B.An alternating direction method for operator equations[J].J Soc Indust Appl Math(SIAM),1964,12(4):848—854. doi: 10.1137/0112072 -
计量
- 文章访问数: 2899
- HTML全文浏览量: 163
- PDF下载量: 649
- 被引次数: 0
下载:
渝公网安备50010802005915号