Numerical solution and stability of multistep method for solving delay differential equations

Abstract

This paper considers the numerical solution of delay differential equations. The predictor–corrector scheme based on generalized multistep methods are implemented in variable order variable stepsize techniques. The formulae are represented in divided difference form where the integration coefficients are computed by a simple recurrence relation. This representation produces simpler calculation as compared with the modified divided difference form, but no sacrifice is made in efficiency and accuracy of the method. Numerical results prove that the method is reliable, efficient and accurate. The P- and Q-stability regions for a fixed stepsize of the predictor–corrector scheme are illustrated for various orders.