Decision-making is a basic cognitive function that includes alternative assessment, the incorporation of information and choosing an appropriate action when uncertainty exists. In this study, the mathematical modeling framework of differential equations and computational methods are used to analyze the decision making process in cognitive science. The proposed model accounts for interactions between cognitive parameters, such as stimulus strength, evidence accumulation, evidence threshold, memory influence and uncertainty about the decision. Temporal dynamics of cognitive states are mathematically described and behavioural reaction is predicted. Sensitivity analysis is used to assess the impact of the important parameters on the decision making process, and numerical techniques are used to give approximate solutions for the complicated dynamics of the model. A computational algorithm is designed to predict systematically decisions made under different cognitive conditions. The results of the simulations show the impact of the parameter variations on decisions accuracy, response behaviour and convergence behaviour. The framework offers a quantitative method of understanding cognitive mechanisms, and can be used to facilitate computational investigations of human decision behaviour under various experimental conditions.