Runge-Kutta methods for first-order periodic boundary value differential equations with piecewise constant arguments (Q1034654)

The authors investigate the numerical solution of Runge-Kutta methods for the solution \[ x'(t)+ ax(t)+ a_0x([t])= \sigma(t), \] \(x(0)= x(T)+\lambda\), where \(T> 0\), \(a\), \(a_0\), \(\lambda\) are real constants, and show the numerical solution is of order \(p\) for the \(p\)th order Runge-Kutta method. Some properties of these numerical solutions with the stability function which is given by the \((r,s)\)-Padé approximation to \(e^z\) are presented. Some experiments are given.