Asymptotic stability of Runge–Kutta methods for nonlinear differential equations with piecewise continuous arguments

• X. Liu ^[1] ; M.Z. Liu ^[2]
  1. [1] Liaocheng University

     Liaocheng University

     China

     
  2. [2] Harbin Institute of Technology

     Harbin Institute of Technology

     China

     
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 280, Nº 1 (15 May 2015), 2015, págs. 265-274
• Idioma: inglés
• DOI: 10.1016/j.cam.2014.11.059
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• Resumen

  • This paper deals with the asymptotic stability of numerical solutions for differential equations with piecewise continuous arguments (EPCAs). The necessary and sufficient condition is given for non-confluent Runge–Kutta methods to preserve the stability of nonlinear scalar EPCAs. As for systems, we prove that some algebraically stable methods can preserve the asymptotic stability.