Higher-Order Multiplicative Derivative Iterative Scheme to Solve the Nonlinear Problems

Grossman and Katz (five decades ago) suggested a new definition of differential and integral calculus which utilizes the multiplicative and division operator as compared to addition and subtraction. Multiplicative calculus is a vital part of applied mathematics because of its application in the areas 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 a detailed convergence analysis of our scheme with the help of a multiplicative calculus approach rather than the normal one. Different kinds of numerical comparisons have been suggested and analyzed. The obtained results (from line graphs, bar graphs and tables) are very impressive compared to the earlier iterative methods of the same order with the ordinary derivative. Finally, the convergence of our technique is also analyzed by the basin of attractions, which also supports the theoretical aspects.