Numerical Study of a Multidimensional Dynamic Quantum Model Arising in Cognitive Psychology Especially in Decision Making

In this research, we propose a new method to approximate the solutions of a multidimensional dynamic quantum model named the nonlinear Schrödinger equations arising in cognitive psychology and decision making. The \( \theta\)-weighted scheme is applied to discretize the time space. Afterwards, the collocation method based on Chebyshev orthogonal polynomials is implemented for solving the equations. Using the proposed method, the equations are converted to a system of linear algebraic equations. In addition, the accuracy and effectiveness of our method are investigated through different examples. The proposed method is compared with the other approaches. The results shows high precision, while having an acceptable runtime.