On the Convergence of Solutions to Dynamic Equations on Time Scales

Nguyen Thu Ha ^[1] ; Nguyen Huu Du ^[3] ; Le Cong Loi ^[3] ; Do Duc Thuan ^[2]
1. [1] Electric Power University
  
  Electric Power University
  
  Vietnam
2. [2] Hanoi University of Science and Technology
  
  Hanoi University of Science and Technology
  
  Vietnam
3. [3] Vietnam National University (Vietnam)
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Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 15, Nº 2, 2016, págs. 453-469
Idioma: inglés
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Resumen
- In this paper, we study the convergence of solutions to dynamic equations x = f (t, x) on time scales{Tn}∞ n=1 when this sequence converges to the time scaleT.
  
  The convergent rate of solutions is estimated when f satisfies the Lipschitz condition in both variables. By a general view, we derive a new approach to the approximation of dynamic equations on time scales, especially the Euler method for differential equations. Some examples are given to illustrate our results.