DERIVATION OF A CLASS OF NUMERICAL INTEGRATORS OF ADAMS MOULTON TYPE FOR SOLUTION OF DELAY DIFFERENTIAL EQUATIONS

Abstract

This research work considers a class of numerical integrators with continuous coefficients for solving first order delay differential equations. In the derivation of the integrators, power series has been used as the basis function for the approximate solution of the differential equations. The approximate solution and the corresponding differential system were respectively interpolated and collocated to generate a system of linear equations. Analysis of properties of the derived integrators viz: zero-stability, order, error constant and region of absolute stability were considered. The accuracy and usability of each of the derived methods were confirmed by solving some numerical examples. The results obtained were compared with the results of existing Runge-Kutta methods for delay differential equations used to solve the same problems. The results show superiority in terms of accuracy of the new method over the existing Runge-Kutta methods for delay differential equations.