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

TL;DR

This paper introduces G-Calculus, a new non-Newtonian calculus variant based on geometric operations, and explores its potential applications in numerical analysis.

Contribution

It proposes G-Calculus with a novel approach to value progression, extending non-Newtonian calculus for improved numerical analysis techniques.

Findings

Defined G-Calculus with geometric value progression

Discussed applications in numerical analysis

Compared G-Calculus with existing non-Newtonian calculus

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.