Solving delay differential equations by predictor-corrector method using lagrange and hermite interpolations

Delay differential equations (DDEs) appear naturally in modeling many real life phenomena. DDEs differ from ordinary differential equations since the derivative of the unknown function contains the expression of the unknown function at earlier and present states as well. DDEs that cannot be solved analytically are solved numerically. In this work, we solve DDEs using predictor-corrector multistep method where the corrector is iterated until convergence. The predictor uses the Adams-Bashforth four-step explicit method and the corrector uses Adams-Moulton three-step implicit method. Two types of interpolation polynomials which are Lagrange and Hermite interpolations are used to approximate the delay solutions. The accuracy of the adapted Adams-Bashforth-Moulton methods using these two polynomials is compared.