This paper performs NP-stability of 2-point one block predictor-corrector method to solve neutral delay differential equations. The numerical formula of a neutral delay equation which is analysed for NP-stability is solved using a new 2-point one block predictor-corrector method. In this study, a characteristic polynomial is employed to calculate all the roots of the characteristic equations of the neutral delay linear test equation. Newton’s divided-difference interpolation polynomial method is used to approximate the delay solutions for both retarded and neutral. To improve the convergence of the solution of neutral delay differential equations, a variable step size technique is implemented. Numerical results show the validity and accuracy of the proposed method.

NP-stability region, block method, neutral delay equations, characteristic polynomial.