A Differential Operator Needed in the generation of a numerical Integrator for Environmental Models

Mercy N.N.; Enoch O.O.; Adeniji A.A.; Alakofa C.O.

Mercy N.N. Human Sciences Research Council
Enoch O.O. Department of Mathematics, Federal University Oye-Ekiti, Ekiti State, Nigeria
Adeniji A.A. Department of Mathematics and statistics, Tshwane university of technology, South Africa.
Alakofa C.O. Department of Mathematics, Federal University Oye-Ekiti, Ekiti State, Nigeria

Keywords: Product rule, Leibnitz’s Theorem, Higher Order Derivatives, Mathematical Induction

Abstract

In this research we generate a series method for computing the nth order derivative of a function that depends on five Independent variables by using the Leibnitz’s theorem in the product rule. Further, the theorem that establishes the new method and its proof are presented by using Mathematical Induction. It is established that the new series method does not require the knowledge of the preceding derivative before obtaining the succeeding ones.

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