A Modified 3-Point Adams Block Method of the Variable Step Size Strategy for Solving Neutral Delay Differential Equations

Abstract

A modified 3-point Adams block method of order six (3ABM6)to solve neutral delay differential equations (NDDEs) using variable step size strategy is developed. The approximate solution of the retarded and the neutral terms of the neutral delay differential equations at the grid points is obtained using the Newton divided difference interpolation technique. The proposed method will approximate the solution in each step using the three-points concurrently. To determine the performance of the proposed method, the maximum errors (MAXERR) and total number of function calls (FNC) will be compared with the method of 2-point order six predictor-corrector. The numerical results show that the 3ABM6 reduces the number of function calls and better accuracy in term of MAXERR.

Keywords

• Neutral delay differential equations, Adams block method, Newton interpolation technique, Variable step size technique, concurrently