Stability of Euler-Maclaurin Methods in the Numerical Solution of Equation u′(t) = au(t) plus a0u([t]) plus a1u([t-1])

To study the numerical solution of the delay differential equations with piecewise continuous arguments (EPCA) which are usually emerged in dynamic models and controls of biological systems,signal systems and so forth. High acurate numerical solution and stability analysis for the equation u'(t) = au(t) + a(0)u([t]) + a(1)u([t - 1]) was concerned. The adaptation of the Euler-Maclaurin method was considered,and the stability region for the Euler-Maclaurin methods for the equation was determined. The conditions that the analytic stability region is contained in the numerical stability region are obtained and a numerical experiment is given. The numerical solution can also perserve the stability of the analytic solution.