Applied Mathematics and Mechanics

, Volume 13, Issue 1, pp 91–99 | Cite as

Exponential dichotomies of nonlinear discrete systems and its application to numerical analysis and computation

  • Zhang Wei-jiang
Article
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Abstract

In this pepar we consider the upwind difference scheme of a kind of boundary value problems for nonlinear, second order, ordinary differential equations. Singular perturbation method is applied to construct the asymptotic approximation of the solution to the upwind difference equation. Using the theory of exponential dichotomies we show that the solution of an order-reduced equation is a good approximation of the solution to the upwind difference equation except near boundaries. We construct correctors which yield asymptotic approximations by adding them to the solution of the order-reduced equation. Finally, some numerical examples are illustrated.

Key words

Nonlinear difference equation singular perturbation exponential dichotomy 
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Copyright information

© Shanghai University of Technology (SUT) 1992

Authors and Affiliations

  • Zhang Wei-jiang
    • 1
  1. 1.Dept. of Applied MathematicsShanghai Jiaotong UniversityShanghai

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