An Effective Iteration Method for a Class of Nonlinear Singular Perturbed Problems

• Wang, Xiaoyun ^[1] ; Pan, Yuyang ^[1] ; Bai, Liang ^[1]
  1. [1] Taiyuan University of Technology

     Taiyuan University of Technology

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 17, Nº 1, 2018, págs. 155-175
• Idioma: inglés
• DOI: 10.1007/s12346-017-0240-5
• Enlaces
  • Texto completo
• Resumen

  • In this paper we investigate a class of singular perturbed differential equations with initial conditions. Based on the equations cannot solved easily by the traditional methods, we give a simple but effective method for finding their approximate periodic solutions firstly. That is, we introduce an iterative technique to the singular perturbed nonlinear system and then adopt the classical perturbed technique to give the approximate solutions. Secondly, some typical examples given to illustrate the methods is a useful tool in solving the nonlinear singular perturbed systems. At last, we present a windowing technique for the system. The convergence processes can be speeded up when we take the windowing technique. These methods can be easily extended to other nonlinear systems and found widely applicable in engineering.

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