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Convergence and Stability in Collocation Methods of Equation u′(t) = au(t) + bu([t])

Author

Listed:
  • Han Yan
  • Shufang Ma
  • Yanbin Liu
  • Hongquan Sun

Abstract

This paper is concerned with the convergence, global superconvergence, local superconvergence, and stability of collocation methods for u′(t) = au(t) + bu([t]). The optimal convergence order and superconvergence order are obtained, and the stability regions for the collocation methods are determined. The conditions that the analytic stability region is contained in the numerical stability region are obtained, and some numerical experiments are given.

Suggested Citation

  • Han Yan & Shufang Ma & Yanbin Liu & Hongquan Sun, 2012. "Convergence and Stability in Collocation Methods of Equation u′(t) = au(t) + bu([t])," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:125926
    DOI: 10.1155/2012/125926
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    References listed on IDEAS

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    1. S. M. Shah & Joseph Wiener, 1983. "Advanced differential equations with piecewise constant argument deviations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 6, pages 1-33, January.
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    Cited by:

    1. Tao Fang & Jitao Sun, 2013. "Stability Analysis of Complex‐Valued Nonlinear Differential System," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).

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