Numerical Stability of Differential Equations with Piecewise Constant Arguments of Mixed Type

Abstract:

      This paper deals with the stability analysis of the Euler-Maclaurin method for differential equations with piecewise constant arguments of mixed type. The expression of analytical solution is derived and the stability regions of the analytical solution are given. The necessary and sufficient conditions under which the numerical solution is asymptotically stable are discussed. The conditions under which the analytical stability region is contained in the numerical stability region are obtained and some numerical examples are given.