奇异摄动反应扩散问题的高阶不等距计算方法

蔡新; 蔡丹琳; 吴瑞潜; 谢康和

奇异摄动反应扩散问题的高阶不等距计算方法

浙江科技学院理学院,杭州 310027;2.泉州师范学院理工学院,福建泉州 362000;3.浙江大学建工学院, 杭州 310027

基金项目: 国家自然科学基金资助项目(50679074);福建省教育厅基金资助项目(JA08140,A0610025);浙江科技学院科研启动基金资助项目(2008050)

详细信息

作者简介:
蔡新(1964- ),男,福建泉州人,教授,博士(联系人.Tel/Fax:+86-592-6182935;E-mail:cxxm05@126.com).

中图分类号: O241.81
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出版历程
- 收稿日期: 2008-06-25
- 修回日期: 2008-12-04
- 刊出日期: 2009-02-15

High Accurate Non-Equidlstant Method for Singular Perturbation Reaction-Diffusion Problem

School of Science, Zhejiang University of Science and Technology, Hangzhou 310027, P. R. China;

摘要

摘要: 考虑奇异摄动反应扩散方程,这是一个多尺度问题,问题在左右两边皆产生边界层现象．根据边界层的奇性,提出不等距的有限差分格式,其主要思想是根据Shishkin过渡点将区域分为边界层区域和边界层外区域,在边界层外采用等距的大步长,在边界层区域内逐步增加网格步长,有一半的网格步长是不同的．进行了截断误差估计,并证明所提方法是稳定的,一致收敛性高于2阶.最后给出数值例子以说明理论结果的正确性．
- 奇异摄动 /
- 反应扩散 /
- 一致收敛 /
- 高阶 /
- 不等距
Abstract: Singular pertubation reaction-diffusion problem with Dirichlet boundary condition is considered. this is a multi-scale problem. The presence of small parameter leads to bomdary Dyer phenomena on both sides of region. Non-equidistant finite difference method wag presented according to the property of boundary layer. The region was divided into the inner botmdary layer region and the outside botutdaty layer regiart according to transition point of Shishkin. The step length is equidistant on the outside bowdaty layer region. The step length is gradually increased on the inner boiutdacy layer region such that half of the step length is digerent firm each other. Tnutcation error was estimated. The new method is stable and uniform convergence with order higher than 2. Finally, numerical results were given, which are in agreement with the theoretical result.
- singular perturbation /
- reaction-diffusion /
- uniform convergence /
- highly accurate /
- non-equidistant

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参考文献(14)

[1]	Farrell P, Hegarty A F, Miller J J H,et al. Robust Computational Techniques for Boundary Layers[M]. Boca Raton: Chapman and Hall/CRC, 2000.
[2]	Miller J J H, O'Riordan E, Shishkin G I.Fitted Numerical Methods for Singular Perturbation Problems[M].Singapore: World Scientific, 1996.
[3]	蔡新. 具有周期边界的守恒型方程的守恒型差分格式[J]. 应用数学和力学, 2001, 22(10):1092-1096.
[4]	CAI Xin, LIU Fa-wang. Uniform convergence difference schemes for singularly perturbed mixed boundary problems[J].Journal of Computational and Applied Mathematics,2004,166(1):31-54. doi: 10.1016/j.cam.2003.09.038
[5]	CAI Xin, LIU Fa-wang. A Reynolds uniform scheme for singularly perturbed parabolic differential equation[J].ANZIAM J,2007,47(5):633-648.
[6]	Kellogg R B, Tsan A. Analysis of some difference approximations for a singular perturbation problem without turning points[J].Math Comp,1978,26(12):1025-1039.
[7]	Bakhvalov N S. On the optimization of methods for boundary-value problems with boundary layers[J].USSR Computational Mathematics and Mathematical Physics,1969,9(4):139-166.
[8]	Jayakumar J. Improvement of numerical solution by boundary value technique for singularly perturbed one dimensional reaction diffusion problem.[J].Applied Mathematics and Computation,2003,142(2):417-447. doi: 10.1016/S0096-3003(02)00312-0
[9]	Beckett G, Mackenzie J A. On a uniformly accurate finite difference approximation of a singularly perturbed reaction-diffusion problem using grid equidistribution[J].Journal of Computational and Applied Mathematics,2001,131(1):381-405. doi: 10.1016/S0377-0427(00)00260-0
[10]	Stynes M, Roos H G. The midpoint upwind scheme[J].Appl Numer Math,1997,23(3):361-374. doi: 10.1016/S0168-9274(96)00071-2
[11]	Stynes M, Tobiska L. A finite difference analysis of a streamline diffusion method on a Shishkin mesh[J].Numer Algorithms,1998,18(3):337-360. doi: 10.1023/A:1019185802623
[12]	Rashidiniab J, Ghasemia M, Mahmoodi Z. Spline approach to the solution of a singularly-perturbed boundary value problems[J].Applied Mathematics and Computation,2007,189(1):72-78. doi: 10.1016/j.amc.2006.11.067
[13]	Clavero C, Gracia J. High order methods for elliptic and time dependent reaction-diffusion singularly perturbed problems[J].Applied Mathematics and Computation,2005,169(1):1109-1127.
[14]	Cen Z D. A hybrid difference scheme for a singularly perturbed convection-diffusion problem with discontinuous convection coefficient[J].Applied Mathematics and Computation,2005,169(1):689-699. doi: 10.1016/j.amc.2004.08.051

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奇异摄动反应扩散问题的高阶不等距计算方法

作者简介:
蔡新(1964- ),男,福建泉州人,教授,博士(联系人.Tel/Fax:+86-592-6182935;E-mail:cxxm05@126.com).

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High Accurate Non-Equidlstant Method for Singular Perturbation Reaction-Diffusion Problem

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奇异摄动反应扩散问题的高阶不等距计算方法

作者简介: 蔡新(1964- ),男,福建泉州人,教授,博士(联系人.Tel/Fax:+86-592-6182935;E-mail:cxxm05@126.com).

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出版历程

High Accurate Non-Equidlstant Method for Singular Perturbation Reaction-Diffusion Problem

计量

出版历程

目录

作者简介:
蔡新(1964- ),男,福建泉州人,教授,博士(联系人.Tel/Fax:+86-592-6182935;E-mail:cxxm05@126.com).