مشخصات پژوهش

‎Functional integral equations (FIEs) arise in many scientific and engineering problems, particularly in control theory, biological systems, viscoelasticity, and population dynamics. The inclusion of state-dependent delays makes these equations highly nonlinear and analytically intractable. Exact solutions are rarely obtainable, thus necessitating robust and efficient numerical approaches.‎ ‎ Traditional numerical methods (fixed collocation, perturbation techniques, finite differences) often fail to capture the accuracy required when delays depend explicitly on the evolving state of the system. These methods can suffer from instability, slow convergence, or high computational costs. Hence, there is a clear need for adaptive schemes tailored to the changing nature of the delay.‎