解含转向点问题的完全指数型拟合差分方法

陈明伦; 王国英

解含转向点问题的完全指数型拟合差分方法

陈明伦¹,
王国英²

1.
重庆交通学院;
2.
南京大学

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出版历程
- 收稿日期: 1988-05-05
- 刊出日期: 1990-01-15

Completely Exponentially Fitted Finite Difference Methods for Problems of Turning Point

Chen Ming-lun¹,
Wang Guo-ying²

1.
Chongqing Jiaotong Institute, Chongqing;
2.
Nanjing University, Nanjing

摘要

摘要: 本文对含转向点的微分方程边值问题建立了完全指数型拟合差分格式,证明了此格式具有一阶一致收敛性.推广了Miller^[1]的方法,简化了证明过程.数值结果表明本格式比Il'in^[2]格式要好.

Abstract: In this paper we construct a completely exponentially fitted finite difference scheme for the boundary value problem of differential equation with turning points, extending Miller's method^[1] and simplifying the method of the proof. We prove the first order uniform convergence of the scheme. The numerical results show that it is better than Il'in's scheme.

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参考文献(13)

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[2]	Il'in,A.M.,Differencing scheme for a differetial equation with a small parameter affecting the highest derivative,Math.Notes Acad.Sci.,USSR.6(1969),596-602.
[3]	Miller,J.J.H.,Sufficient conditions for the convergence uniformly in ε,of a three-point difference scheme for a singular perturbation problem,Proc.Oberwolfach,Germany,Lecture Notes in Maths.,Springer-Verlag,679(1977),85-91.
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[13]	Jiang Fu-ru,On the boundary value problems for a class of ordinary differential equations with turning points,Appl.Math and Mech.,1,2(1980),201-213.