A Uniformly Convergent Difference Scheme for the Singular Perturbation of a Self-adjoint Elliptic Partial Differential Equation

Liu Fa-wang; Zheng Xiao-su

Volume 7 Issue 5

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Article Navigation > Applied Mathematics and Mechanics > 1986 > 7(5): 457-465

Liu Fa-wang, Zheng Xiao-su. A Uniformly Convergent Difference Scheme for the Singular Perturbation of a Self-adjoint Elliptic Partial Differential Equation[J]. Applied Mathematics and Mechanics, 1986, 7(5): 457-465.

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A Uniformly Convergent Difference Scheme for the Singular Perturbation of a Self-adjoint Elliptic Partial Differential Equation

Liu Fa-wang¹,
Zheng Xiao-su²

1.
Fuzhou University, Fuzhou;
2.
Fujian Teachers' University, Fuzhou

Received Date: 1984-01-20
Publish Date: 1986-05-15

Abstract

Abstract

In this paper,we consider a self-adjoint elliptic first boundary value problem with a small parameter affecting the highest derivative.In the paper,we set up a new scheme by the asymptotic analysis method,compare asymptotic behavior between the solution of the difference equation and the solution of the differential equation,and show uniform convergence of the new scheme.

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References

[1]	Doolan,E.P.,J.J.H.Miller and W.H.A.Schilders,Uniform Numerical Method for Problems with Initial and Boundary Laye.(1980).
[2]	苏煜城、吴启光,椭圆一抛物偏微分方程奇异摄动问题的差分解法,应用数学和力学.1,2(1980).
[3]	苏煜城.奇异摄动中的边界层校正法,上海科学技术出版社(1983).