One-step implicit methods or solving delay differential equations

Abstract

Two one-step implicit methods—the second order Trapezium method and the fourth order implicit Runge-Kutta method for solving the delay differential equations (DDE) are developed. The significance of implicit methods lie in their 4-stability for ordinary differential equations. Different techniques are used to approximate the delay term. We also discuss the local truncation error estimate. Numerical examples are solved to show the effectiveness of the methods so developed.