A class of odd order numerical integrators and its applications to the study of nature and location of singularity of non-autonomous initial value problems and their applications to climate change

Abstract

Even though, there a number of environmental models that seek to evaluate arbitrary even (odd) number of nodes in climate change problems, in this research, we seek to present a method of obtaining a trigonometric interpolation polynomial through polynomial interpolation. A class of formulae for the numerical solution of Initial Value Problems (IVP), in Ordinary Differential Equations (ODEs) is considered. This class of integrators is imbedded with the capacity of determining the nature and location of catastrophe in a system of IVP that is non-autonomous in nature. The study firstly, presents the method to compute a trig-polynomial interpolation, with a specific focus on the coefficients of the trigonometric polynomial, also the derivation of odd numerical integrators. Subsequently, discussions on the numerical solutions of the problem using the study approach is presented by implementing the numerical integrators to non-autonomous initial value problems. The numerical schemes afford us the opportunity to control the performance of schemes because of the two complex function control parameters. Lastly, performance of the proposed methods is assessed using analytical numerical simulations. Results from the proposed methods are compared with observed data and found compare favorably well. Owing to these results, the proposed methods can be used in both theoretical and practical applications of solving climate change problems. Moreover, these integrators can be developed into user friendly software that can be used to study the frequency of global emissions, excitation energies of the molecular composition of components that contribute to climate changes.