Lin Peng-cheng, Guo Wen. The Uniformly Convergent Difference Schemes for a Singular Perturbation Problem of a Self-Adjoint Ordinary Differential Equation[J]. Applied Mathematics and Mechanics, 1989, 10(1): 33-41.
 Citation: Lin Peng-cheng, Guo Wen. The Uniformly Convergent Difference Schemes for a Singular Perturbation Problem of a Self-Adjoint Ordinary Differential Equation[J]. Applied Mathematics and Mechanics, 1989, 10(1): 33-41.

# The Uniformly Convergent Difference Schemes for a Singular Perturbation Problem of a Self-Adjoint Ordinary Differential Equation

• Publish Date: 1989-01-15
• In this paper, we construct a class of difference schemes with fitted factors for a singular perturbation problem of a self-adjoint ordinary differential equation. Using a different method from [1], by analyzing the truncation errors of schemes, we give the sufficient conditions under which the solution of lite difference scheme converges uniformly to the solution of the differential equation. From this we propose several specific schemes under weaker conditions, and give much higher order of uniform convergence, and applying them to example, obtain the numerical results.
•  [1] Doolan,E.P,J.J.H.Miller and W.H.A.Schilders,Uniform Numerical Methods for Problemswith Initial and Boundary Layers,Dublin,Boole Press(1980). [2] 林鹏程、郭雯,《奇异摄动问题数值解法》,讲义. [3] Il'in,A.M.,Difference scheme for a differential equation with a small parameter affecting highest derivative.Math.Notes,6(1969),596-692. [4] Protter,M.A.and H.F.Weinberger,Maximum Principles in Differential Equations.Prentice Hall.Englewood.Cliffs.N.J.(1967). [5] Kellogg,R.B.and A.Tsan,Analysis of some difference approximations for a singular perturbation problem without turning points,Math.Comp.32(1978),1025-1039.

### Catalog

###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142