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

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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.

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Authors and Affiliations

  1. Dept. of Applied Mathematics, Shanghai Jiaotong University, Shanghai

    Zhang Wei-jiang

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  1. Zhang Wei-jiang
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Communicated by Su Yu-cheng

Project supported by the National Natural Science Foundation of China and Excellent Young Teachers Foundation of Education Commission of China.

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Wei-jiang, Z. Exponential dichotomies of nonlinear discrete systems and its application to numerical analysis and computation. Appl Math Mech 13, 91–99 (1992). https://doi.org/10.1007/BF02450431

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  • DOI: https://doi.org/10.1007/BF02450431

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