## 留言板

G. M. 艾米雷利耶弗, 哈基杜柔. 奇异摄动初值问题的一致收敛有限差分法[J]. 应用数学和力学, 1999, 20(4): 363-370.
 引用本文: G. M. 艾米雷利耶弗, 哈基杜柔. 奇异摄动初值问题的一致收敛有限差分法[J]. 应用数学和力学, 1999, 20(4): 363-370.
G. M. Amiraliyev, Hakk Duru. A Uniformly Convergent Finite Difference Method for a Singularly Perturbed Initial Value Problem[J]. Applied Mathematics and Mechanics, 1999, 20(4): 363-370.
 Citation: G. M. Amiraliyev, Hakk Duru. A Uniformly Convergent Finite Difference Method for a Singularly Perturbed Initial Value Problem[J]. Applied Mathematics and Mechanics, 1999, 20(4): 363-370.

## 奇异摄动初值问题的一致收敛有限差分法

• 中图分类号: O175.1;O241.81

## A Uniformly Convergent Finite Difference Method for a Singularly Perturbed Initial Value Problem

• 摘要: 通过一阶和二阶导数讨论了带小参数的线性二阶常微分方程的初值问题.在均匀网格上得出了带常数拟合因子的指数型拟合差分格式,给出了离散最大模意义上的一阶一致收敛性.文中给出了数值结果.
•  [1] O' Malley R E,Jr.Introduction to Singular Perturbations[M].New York:Academic Press,1974. [2] O'Malley R E,Jr.Singular Perturbation Methods for Ordinary Differential Equations[M].New York:Springer-Verlag,1991. [3] Neyfeh A H.Perturbation Methods[M].Wiley,1973. [4] 苏煜城,林平.具有零阶退化方程的二阶双曲型方程奇异摄动问题的一致差分格式[J].应用数学和力学,1990,11(4):283~294. [5] Boglaev I P.Numerical integration of an initial value problems for a systems with a small parameter affecting the derivative[J].USSR Comput Math Mac Pys,1987,27:63~75.(in Russian) [6] Doolan E P,Miller J J H,Schilders W H A.Uniform Numerical Methods for Problems with Initial and Boundary Layers[M].Dublin:Boole Press,1980. [7] Amiraliyev G M.Difference schemes on the uniform mesh for singular perturbed pseudo-parabolic equations[J].Turkish J Math,1995,19:207~222. [8] Amiraligev G M.On difference schemes for problems of the theory of dispersive waves[J].Soviet Math Dokl,1991,42:235~238. [9] Amiraliyev G M.Difference method for the solution of one problem of the theory dispersive waves[J].Differential Equations,1990,26:2146~2154.(in Russian) [10] Samarski A A.Theory of Difference Schemes[M].2nd Ed.Moscow:“Nauka”,1983;German transl,Leibzig:Geest Portig,1984.

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##### 出版历程
• 收稿日期:  1997-11-25
• 刊出日期:  1999-04-15

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