Higher-order multiplicative derivative iterative scheme to solve the
nonlinear problems
Abstract
Grossman and Katz (five decade ago) suggested a new definition of
differential and integral calculus which utilize the multiplicative and
division operator as compared to the addition and subtraction.
Multiplicative Calculus is a vital part of the applied Mathematics
because of its application in the area of Biology, Science and Finance,
Biomedical, Economic, etc. Therefore, we used a multiplicative calculus
approach to develop a new fourth-order iterative scheme for multiple
roots based on the well-known King’s method. In addition, we also
propose the detailed convergence analysis of our scheme with the help of
multiplicative calculus approach rather than the normal one. Different
kinds of numerical comparisons has been suggested and obtained results
are very impressive as compared to the ordinary derivative methods.
Finally, the convergence of our technique is also analyzed by basin of
attractions that also support the theoretical aspects.