A Mathematical Model to Analyze the Impact of Using Solar Energy Instead of Fossil Fuel in Reducing Global Warming

Abstract

The importance of fossil fuel in our day-to-day life cannot be described in words. Worldwide fossil fuel usage amounted to around 128,550 terawatts per hour. Keeping all the necessity of fossil fuel in our daily life, we cannot deny the fact that the vast usage of fossil fuel is one of the most vital reasons behind global warming and climate change. Many reports claim that the global temperature has increased by 1°C dues to excessive usage of fossil fuels. Moreover, the resources of fossil fuel are limited and humanity may run out of these limited resources in the future. In order to reduce global warming, in this study, we are proposing to increase the usage of solar energy instead of fossil fuel using mathematical modeling techniques. We have formulated a three-compartmental model with the compartments Global Temperature, Fossil Fuel Consumption and Solar Energy Consumption with interactions between the compartments. We have conducted both qualitative and numerical analysis of the model. The qualitative analysis includes the study of equilibrium, stability, nature of the stability at the equilibrium points. From the results of the numerical analysis, we can conclude that increasing the usage of solar systems can effectively reduce global warming. In countries like Bangladesh, the vast implementation of solar energy can be more effective than in other countries as the average temperature remains quite higher than in other countries, also for the availability of enough sunlight.