Behind an Iterative Scheme: Is the Iterative Scheme a tool for Sustainable Development?

Abstract

Contrary to the thought that Mathematics and Sustainable Development are unconnected, Mathematical tools are veritable means of solving complex nonlinear models that arises from the field of science, environment, economics and engineering. Obtaining the solution of nonlinear models is key and necessary to evaluate sustainability in quantitative terms. But, some of these nonlinear models are unsolvable via analytic means, hence numerical iterative procedures are utilised.  However, the efficiency of an iterative procedure for solving mathematical models is a function of time and cost, which are key factors that cannot be undermined in achieving Sustainable Development. One golden rule in the development of new iterative schemes for solving nonlinear models, is that it should be of low computation cost. The presence of functions derivatives evaluations in an iterative scheme no doubt, increases its implementation cost. More so, obtaining derivative of some complex functions can be big challenge. In this regard, three class of fourth, seventh and eight-order derivative free iterative structures are developed and put forward in this work. The convergence test on the developed iterative scheme were established using some designed computer programs that are executed in MATHEMATICA software environment. To verify the schemes as tools for sustainable economic development, some recently modelled physical phenomena were solved using the developed iterative schemes and their results were placed in juxtaposition with that of some existing contemporary schemes.