Numerical Schemes for Fractional Energy Balance Model of Climate Change with Diffusion Effects

This study aims to propose numerical schemes for fractional time discretization of partial differential equations (PDEs). The scheme is comprised of two stages. Using von Neumann stability analysis, we ensure the robustness of the scheme. The energy balance model for climate change is modified by adding source terms. The local stability analysis of the model is presented. Also, the fractional model in the form of PDEs with the effect of diffusion is given and solved by applying the proposed scheme. The proposed scheme is compared with the existing scheme, which shows a faster convergence of the presented scheme than the existing one. The effects of feedback, deep ocean heat uptake, and heat source parameters on global mean surface and deep ocean temperatures are displayed in graphs. The current study is cemented by the fact-based popular approximations of the surveys and modeling techniques, which have been the focus of several researchers for thousands of years.