A New Alternating Group Explicit-Implicit Algorithm With Highly Accuracy for the Dispersive Equation

ZHANG Qing-jie; WANG Wen-qia

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Article Navigation > Applied Mathematics and Mechanics > 2008 > 29(9): 1107-1116

ZHANG Qing-jie, WANG Wen-qia. A New Alternating Group Explicit-Implicit Algorithm With Highly Accuracy for the Dispersive Equation[J]. Applied Mathematics and Mechanics, 2008, 29(9): 1107-1116.

Citation:

ZHANG Qing-jie, WANG Wen-qia. A New Alternating Group Explicit-Implicit Algorithm With Highly Accuracy for the Dispersive Equation[J]. Applied Mathematics and Mechanics, 2008, 29(9): 1107-1116.

Citation:

ZHANG Qing-jie, WANG Wen-qia. A New Alternating Group Explicit-Implicit Algorithm With Highly Accuracy for the Dispersive Equation[J]. Applied Mathematics and Mechanics, 2008, 29(9): 1107-1116.

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A New Alternating Group Explicit-Implicit Algorithm With Highly Accuracy for the Dispersive Equation

School of Mathematics, Shandong University, Jinan 250100, P. R. China

Received Date: 2007-11-20
Rev Recd Date: 2008-08-01
Publish Date: 2008-09-15

Abstract

Abstract

A new alternating group explicit-implicit scheme (nAGEI) for the dispersive equation with a periodic boundary condition is derived. This new unconditionally stable scheme has the fourth-order truncation error in space and quicker ratio of convergence than some known alternating group methods (eg. ASEI and AGE). A comparison of the accuracy of this method with some prior ASEI and AGE methods is showed in the numerical experiment.
- dispersive equation,
- finite difference,
- alternating group explicit-implicit method (nAGEI),
- high accuracy,
- unconditional stability,
- parallel computation

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References(16)

References

[1]	QIN Meng-zhao.Difference schemes for the dispersive equation[J].Computing,1983,31(3):261-267. doi: 10.1007/BF02263436
[2]	林鹏程.色散方程ut=auxxx的一类具高稳定性三层格式[J]. 应用数学和力学,1988,9(9):803-808.
[3]	黎益.色散方程的四点显式差分格式[J].应用数学和力学,1993,14(3):219-223.
[4]	Wazwaz A M. An analytic study on the third-order dispersive partial differential equation[J].Appl Math Comput,2003,142(2/3):511-520. doi: 10.1016/S0096-3003(02)00336-3
[5]	ZHU Shao-hong,YUAN Guang-wei,SHEN Long-jun.Alternating group explicit method for the dispersive equation[J].Intern J Comp Math,2000,75(1): 97-105. doi: 10.1080/00207160008804967
[6]	ZHU Shao-hong,Zhao J.The alternating segment explicit-implicit method for the dispersive equation[J].Applied Mathematics Letters,2001,14(6): 657-662. doi: 10.1016/S0893-9659(01)80022-7
[7]	王文洽.色散方程的一类新的并行交替分段隐格式[J]. 计算数学,2005,27(2): 129-140.
[8]	Dawson C N,DU Qiang,Dupont T F.A finite difference domain decomposition algorithm for numerical solution of the Heat equation[J]. Mathematical Computation,1991,57(195): 63-71. doi: 10.1090/S0025-5718-1991-1079011-4
[9]	YUAN Guang-wei,ZHU Shao-hong,SHEN Long-jun.Domain decomposition algorithm based on the group explicit formula for the heat equation[J].International Journal of Computer Mathematics,2005,82(10):1295-1306. doi: 10.1080/0020716042000301824
[10]	Evans D J,Abdullah A R B.Group explicit methods for parabolic equations[J].Intern J Computer Math,1983,14(1): 73-105. doi: 10.1080/00207168308803377
[11]	Evans D J,Abdullah A R B.A new explicit method for the diffusion-convection equation[J].Comp Math Appl,1985,11(1/3):145-154. doi: 10.1016/0898-1221(85)90143-9
[12]	ZHANG Bao-lin.Alternating segment explicit-implicit method for diffusion equation[J].J Numer Meth Compt Appl,1991,12(4):245-251.
[13]	ZHANG Bao-lin,Li W. On alternating segment Crank-Nicolson scheme[J].Parallel Computing,1994,20(8):897-902. doi: 10.1016/0167-8191(94)90123-6
[14]	LU Jin-fu,ZHANG Bao-lin,ZUO Feng-li.Modified AGE methods for the convection-diffusion equation[J].Communications in Numerical Methods in Engineering,1998,14(1):65-75. doi: 10.1002/(SICI)1099-0887(199801)14:1<65::AID-CNM127>3.0.CO;2-P
[15]	曲富丽，王文洽.三阶非线性KdV方程的交替分段显-隐差分格式[J].应用数学和力学，2007,28(7):869-876.
[16]	Kellogg R B.An alternating direction method for operator equations[J].SIAM J Soc Indust Appl Math,1964,12(4): 848-854. doi: 10.1137/0112072