Numerical investigation for religious affiliation population dynamics model

Numerical investigation for religious affiliation population dynamics model

The curiosity of analyzing the impact of religious affiliation among different social communities in the modern era can derive significant contribution in terms of the role played by religion in human lives. To facilitate the investigation, a fully connected net¬work represented by a set of ordinary differential equations (ODEs) reflects the religious affiliation population dynamics (RAPD) model is analyzed. The RAPD system comprising of three subpopulations: committed religious (CR), non-committed religious (NCR) and non-religious (NR) individuals. Transitions among these groups as well as spontaneous shifts are governed by probabil¬ity based on social interactions. The efficacy of the Adams predictor-corrector method is exploited to generate the reference data set that portrays the real-world data dynamics. The reference data set is utilized as the benchmark for the actual data where case studies along with their related cases are formulated by varying the values of RAPD’s parameters i.e., the probabilities of social pressures and spontaneous evolution. The comparative analysis is presented with the aid of employing various numerical techniques including backward differentiation formula (BDF), explicit and implicit Runge-Kutta (RK) to trace transitions and trends assessing absolute error (AE) in numerical results. For the purpose of evaluating the outcomes in terms of the accuracy, efficiency and robustness, solu¬tion plots illustrations along with the AE metric is presented. The efficiency in the performance of the various numerical techniques is reflected via AE values that shows that even the maximum error is negligible and below 10-7.