Parameter Class for Solving Delay Differential Equations

Abstract

In this paper a parameter class of Linear multistep method are applied to solve delay differential equations of the form y’(t) = f(t; y(t); y(t- t(t))), (t >0) subject to the initial condition y(t) = j (t) for t_min =<t <= 0 , t > 0 . The stability properties when the methods were applied to the test equation with a fixed delay t ; y’(t) = λy(t) + µy(t - t ); t ³ 0; are studied λ; µ are complex constants and Ф(t) is a continuous complex-valued function. The stability regions are plotted and numerical results are introduced.