Application of the Quasilinearization Method to Approximate Non-linear Delay Differential Equations in Physical Problems

This paper investigates the application of the Quasilinearization Method (QLM) for approximating non-linear delay differential equations (DDEs), which are prevalent in fields such as control systems and population dynamics. QLM effectively transforms these complex non-linear problems into a system of linear equations, a key advantage for computational efficiency. Our work provides two main contributions: a rigorous mathematical proof demonstrating the quadratic convergence of the proposed technique and numerical examples that illustrate its practical applicability and reliability. We apply QLM to DDEs with various non-linear forms, including quadratic and exponential types and with fixed, discrete delays. The results confirm that the method is highly accurate, computationally efficient and easy to implement, making it  a valuable tool for future research.

کلیدواژه ها:

Delay differential equations ، Quasilinearization method ، Non-linear differential equations ، Lane-Emden type equation