Psychological/Educational Behavioral Modeling Using Dickson Polynomial

This paper develops a dynamic behavioral model describing the evolution of learning and memory through nonlinear differential equations involving three key psychological factors: Awareness (cognitive level), Forgetfulness (knowledge decay) and Stress (negative cognitive influence). The model captures the interplay between internal motivators, natural decline and external stressors that shape memory retention and forgetting. To solve the nonlinear system, two numerical methods are applied: The Adomian-Laplace decomposition method for semi-analytical solutions and a spectral polynomial collocation method using Dickson polynomials with Chebyshev nodes for high-accuracy numerical approximation. Error functions are introduced to rigorously assess solution accuracy. This interdisciplinary work demonstrates the effectiveness of advanced mathematical techniques in modeling complex psychological dynamics, providing a robust computational framework to simulate and analyze learning, memory retention and stress effects over time.

Keywords:

Adomian-Laplace Method , Dickson Polynomials , Chebyshev Collocation point