半线性常微分方程混合边值奇摄动问题的一致差分格式*
A Uniformly Difference Scheme of Singular Perturbation Problem for a Semilinear Ordinary Differential Equation with Mixed Boundary Value Condition
-
摘要: 本文应用分离奇性法研究半线性常微分方程混合边值奇摄动问题的一致差分格式,我们证明了所构造的I1'in型差分格式关于小参数ε的一阶一致收敛性.在本文的最后,我们给出一个数值例子,计算结果与理论分析相符合.Abstract: In the poper, the method of separating singularity is applied to study the uniformly difference scheme of a singular perturbation problem for a semilinear ordinary differential equation with mixed boundary value condition. The uniform convergence on small parameter ε of order one for an Il'in type difference scheme constructed is proved. At the end of the paper, a numerical example is given. The computing results coincide with the theoretical analysis.
-
[1] E,P,Doolan,J.J,H,Miller and W.H,A,Schilders,Uniform Numerical Methods for Problems with Initial and Boundary Lagers,Boole Press,Dublin(1980). [2] R.B,Kellogg and A,Tsan,Analysis of some difference approximations for a singular perturbation problems without turning points,Math,Comp.,32(144)(1978),1025-1039 [3] 蔡新、林鹏程,守恒型奇摄动常微分方程混合边值问题的数值解法,华侨大学学报,11(4)(1990),344-352. [4] 林平、苏煌城.二阶拟线性奇摄动常微分方程的数值解法,应用数学和力学,10(11)(1989),955-959. [5] M,H,Protter and H,F,Weinberger,Maximum Principles in Differential Equations,Springer-Verlag,New York(1984). -
点击查看大图
计量
- 文章访问数: 1893
- HTML全文浏览量: 72
- PDF下载量: 541
- 被引次数: 0
下载:
