Abstract
ABSTRACTMany dynamical systems in physics and engineering are characterized by the property of possessing a bounded absorbing set which all trajectories enter in a finite time and thereafter remain inside. It is highly important to analyse whether or not the numerical methods for solving these dynamical systems inherit such property of the underlying systems. In this paper, it is proved that, under some assumptions, a multistep Runge–Kutta (abbrev. MRK) method is dissipative when it is applied to a class of neutral integro-differential equations with delay, provided it is -algebraically stable. Numerical examples are given to confirm our theoretical results.
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