Some basic properties of G-Calculus and its applications in numerical analysis

Khirod Boruah; Bipan Hazarika

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arXiv · 1607.07749

Some basic properties of G-Calculus and its applications in numerical analysis

Khirod Boruah·Bipan Hazarika

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Abstract

Objective of this paper is to introduce a new type of calculus which will be called G-Calculus based on non-Newtonian calculus introduced by Grossman and Katz \cite{GrossmanKatz}. The basic difference between geometric calculus defined by Grossman and Katz and the present G-calculus is that Grossman took the values of the argument as $x, x+ h, x+2h,...$ but here in G-calculus we take the values as $x, x\oplus h, x\oplus e^2\odot h, x\oplus e^3\odot h....$ This calculus will have great deal with numerical analysis which are discussed in the last section of this paper.

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Khirod Boruah, Bipan Hazarika. 2016-07-24. Some basic properties of G-Calculus and its applications in numerical analysis. https://arxiv.org/abs/1607.07749

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