This paper studies the numerical stability of spline collocation technique for finding the numerical solutions of neutral delay algebraic differential equations (DDEs). The conditions necessary to ensure the widest areas of p-stability of the proposed numerical technique are determined when they are applied to a test problem.
The numerical study of convergence shows that the numerical technique proposed when applied to the test of these equations was consistent and convergent from the order ninth.
The effectiveness of the proposed spline technique was verified by solving four standard problems in both linear and nonlinear cases. The results of numerical comparisons with some other methods indicate the superiority of our results and the most accurate ones.
