An Explicit Numerical Technique for Nonlinear Nonlocal Time-Delay Dynamical Systems via Quadratic Spline Approach

Dynamical systems with delay are widespread in nature. The study of time-delay induced changes in the collective behavior of systems of coupled nonlinear oscillators is a subject of great interest, both because of its fundamental importance from the point of view of dynamical systems and because of its practical applications. In this paper, an explicit technique is proposed for numerical solution of nonlocal dynamical systems with time delay. The proposed method is adopted quadratic spline interpolation. Then, the error analysis of the developed method is discussed. It is exploited in the discussion of nonlocal delay Ikeda and Hutchinson models. Finally, the performance of the presented approach is verified by applying the error and convergence study for different values of fractional order parameters.