Sustainable Development through Iterative Scheme: A Computational Perspective

Abstract

Contrary to the notion that mathematics and sustainable development are unrelated, mathematical tools, particularly numerical iterative procedures, play a vital role in solving complex nonlinear models that arise from various fields, including science, environment, economics, and engineering. These models are crucial for quantitatively assessing sustainability, but some cannot be solved analytically. Therefore, efficient iterative procedures are essential, as they significantly impact time and cost, two critical factors in achieving sustainable development. Minimizing computational cost is a fundamental principle in developing new iterative schemes. Since derivative evaluations increase implementation costs and can be challenging for complex functions, this study presents three classes of derivative-free iterative structures with fourth, seventh, and eighth-order convergence. Using custom-designed computer programs in the MATHEMATICA software environment, we verified the convergence of these schemes. Furthermore, we applied these schemes to recently modeled physical phenomena and compared them to existing contemporary schemes, demonstrating their effectiveness as tools for sustainable economic development.