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

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...

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Bibliographic Details
Published in:arXiv.org 2016-07
Main Authors: Boruah, Khirod, Hazarika, Bipan
Format: Article
Language:English
Subjects:
Calculus
Numerical analysis
Online Access:Get full text
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Summary: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.
ISSN:2331-8422