Apply Linear Multistep Method To Delay Defferential Equation

Many applications of the delay differential equations and the stability results of the analytic solutions and the numerical solutions of the delay differential equations with continuous and discontinuous arguments in the recent years are presented. There is nothing about the linear multistep methods. At first, the easiest the linear multistep methods, 2-Adams explicit method and 3-Adams explicit method are studied. Some numerical experiments show that the original order of the classical method can not be preserved when applying to EPCA. The suitable forms of the two methods are constructed for EPCA, whose order are their original orders. On the base, the convergence of the k -Adams method is discussed. Similarly to 2-Adams explicit method and 3-Adams explicit method, suitable forms of the -Adams explicit method is constructed for EPCA, which preserves the original order. And numerical experiments are given. Finally, the -step linear multistep methods are considered. It is proved that the order of accuracy of the classical -step linear multistep methods can not be larger than 1 when applying to EPCA and the order of accuracy is 1 if and only if the method is the -Adams method. A modified type of the -step linear multistep method is built for EPCA such that the method can preserve the original order. Some numerical experiments show that the modified methods preserve the original order of the classical method when applying to EPCA. kkkkk...