A Uniform High-Order Method for a Singular Perturbation Problem in Conservative Form

Wu Qi-guang; Sun Xiao-di

Volume 13 Issue 10

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Article Navigation > Applied Mathematics and Mechanics > 1992 > 13(10): 873-880

Wu Qi-guang, Sun Xiao-di. A Uniform High-Order Method for a Singular Perturbation Problem in Conservative Form[J]. Applied Mathematics and Mechanics, 1992, 13(10): 873-880.

Citation:

Wu Qi-guang, Sun Xiao-di. A Uniform High-Order Method for a Singular Perturbation Problem in Conservative Form[J]. Applied Mathematics and Mechanics, 1992, 13(10): 873-880.

Citation:

Wu Qi-guang, Sun Xiao-di. A Uniform High-Order Method for a Singular Perturbation Problem in Conservative Form[J]. Applied Mathematics and Mechanics, 1992, 13(10): 873-880.

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A Uniform High-Order Method for a Singular Perturbation Problem in Conservative Form

Department of Mathematics, Nanjing University, Nanjing

Received Date: 1991-09-09
Publish Date: 1992-10-15

Abstract

Abstract

A uniform high-order method is.presented for the numerical solution of a singular perturbation problem in conservative form.We firest replace the original second-order problem (1.1) by two equivalent first-order problems (1.4),i.e.,the solution of (1.1) is a linear combination of the solutions of (1.4).Then we derive a uniformly O(^hm+1) accurate scheme for the first-order problems (1.4),where m is an arbitrary nonnegative integer,so we can get a uniformly O(^hm+1) accurate solution of the original problem (1.1) by relation (1.3).Some illustrative numerical results are also given.
- uniform high-order method,
- singular perturbation problem,
- initial value problem

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References(7)

References

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[3]	Kadalbajoo,M.K.and Y.N.Reddy,An approximate method for solving a class of singular perturbation problems,J.Math.Anal.Appl.,133(1988),306-323.
[4]	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.
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