Efficiency and Sustainability in Simulation: Enhancing Accuracy of Chaotic Maps Using Kahan Summation

Mathematical modelling is essential in scientific research for approximating systems through equations for simulation, prediction, and investigation. While system identification techniques have become popular for obtaining models directly from data, finding an appropriate model for nonlinear systems can be difficult. In particular, conventional model validation approaches are ineffective for chaotic systems. Although numerical simulations are widely used to identify and analyse these mathematical models, less attention has been given to improving simulation accuracy, leading to imprecise results. This work proposes an efficient and sustainable approach to improve the accuracy of chaotic maps by reducing numerical errors and increasing precision during simulations of chaotic polynomial models. The Kahan summation is used to minimise the propagation of computational error, and the results are validated using symbolic computation. The proposed technique increases simulation accuracy, allows more iterates with no loss of digit significance, and represents a way to save energy by requiring less powerful computing. The main contribution of this work is the presentation of an effective method for reducing the influence of numerical errors, a simple mathematical tool with low computational cost. Future investigations could focus on the reduction in LLE despite the Kahan summation not changing the mathematical map.