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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

Mercy Nduku Ngungu, Enoch O. O., Adeniji A. A.

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 also present a method to obtain the 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. 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.


Keywords


Interpolant, trig-polynomial, numerical integrators, non-autonomous IVP’s, singularity, undetermined coefficients.

References


Enoch, O.O.A. and A.A. Olatunji, 2012. A new self-adjusting numerical integrator for the numerical solutions of ordinary differential equations. Global J. Sci. Front. Res., 12: 24-35.

Ibijola, E.A. and O.O. Enoch, 2011. A self-adjusting numerical integrator with an inbuilt switch for discontinuous initial value problems. Aust. J. Basic Appl. Sci., 5: 1560-1565.

Lambert, J.D. and B. Shaw, 1966. A method for the numerical solution of y'= f (x, y) based on a self adjusting non-polynomial interpolant. Math. Comput., 20: 11-20.

Scheiber, E., 2016. On the computation of a trigonometric inter-polation polynomial. Bull. Transilvania Univ. Brasov. Math., Inf., Phys. Ser. III, 9: 153-160.

Scheiber, E., 2011. On the interpolation trigonometric polynomial with an arbitrary even number of nodes. In SYNASC (pp. 71-74)


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