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Applied Mathematics and Mechanics

, Volume 8, Issue 10, pp 929–937 | Cite as

A singular perturbation problem for periodic boundary differential equation

  • Lin Peng-cheng
  • Jiang Ben-xian
Article

Abstract

In this paper, we consider a second order ordinary differential equation with a small, positive parameter ε in its highest derivative for periodic boundary values problem and prove that the solution of difference scheme in paper [1] uniformly converges to the solution of its original problem with order one.

Keywords

Difference Scheme Periodic Boundary Small Parameter Small Neighborhood Positive Parameter 
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References

  1. [1]
    Pejinkina, A.A., Solution of the period problem for second order ordinary differential equation with small parameter in its leading derivatives.Differential Equations with Small Parameter (1980), 111–118. (in Russian)Google Scholar
  2. [2]
    Emelyanov, K.V., A difference method for solving the third boundary problem for a differential equation with small parameter in its leading derivatives,USSR Computational Math. and Math. Phys.,15, 6 (1975), 1455–1463. (in Russian)MathSciNetGoogle Scholar
  3. [3]
    II’in, A.M., Differece schemes for a differential equation with a small parameter affecting the highest derivativeMat. Zametki,6 (1969), 237–248.MathSciNetGoogle Scholar
  4. [4]
    Kellogg, R.B. and A. Tsan, Analysis of some difference approximation for a singular perturbation problem without turning points,Math. Comp.,32 (1978), 1025–1039.zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Shanghai University of Technology (SUT) 1987

Authors and Affiliations

  • Lin Peng-cheng
    • 1
  • Jiang Ben-xian
    • 1
  1. 1.Fuzhou UniversityFuzhou

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