The numerical asymptotically stability of a linear differential equation with piecewise constant arguments of mixed type (Q520178)

This work concerns the numerical stability of certain differential equations with piecewise constant arguments. A closed form expression to the solution for this problem is presented and its asymptotic stability is analysed. By applying Runge-Kutta methods to the differential equation, conditions under which the numerical solution is asymptotically stable are presented. The problem of when the analytical stability region is included in the numerical stability region is characterized. Results of numerical experiments validating the theoretical findings are reported.