On inverse iteration process for finding all roots of nonlinear equations with applications

In this work, we construct a new family of inverse iterative numerical technique for extracting all roots of nonlinear equation simultaneously. Convergence analysis verifies that the proposed family of methods has local 10th-order convergence. Among the test models investigated are blood rheology, a fractional nonlinear equation model, fluid permeability in biogels, and beam localization models. In comparison to other methods, the family of inverse simultaneous iterative techniques gets initial estimations to exact roots within a given tolerance while using less function evaluations in each iterative step. Numerical results, basins of attraction for fractional nonlinear equation, residual graphs are presented in detail for the simultaneous iterative techniques. The newly developed simultaneous iterative techniques were thoroughly investigated and proven to be efficient, robust, and authentic in their domain.