奇异摄动初值问题的一致收敛有限差分法

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名

邮箱

手机号码

标题

留言内容

验证码

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.
- 奇异摄动 /
- 差分格式 /
- 一致收敛 /
- 初值条件 /
- 线性常微分方程
Abstract: Initial value problem for linear second order ordinary differential equation with small parameter by the first and second derivatives is considered.An exponentially fitted difference scheme with constant fitting factors is developed in a uniform mesh,which gives first-order uniform convergence in the sense of discrete maximum norm.Numerical results are also presented.
- singular perturbation /
- difference scheme /
- uniform convergence /
- initial value condition /
- linear ordinary differential equation

[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.