On Computer Implementation for Comparison of Inverse Numerical Schemes for Non-Linear Equations

In this research article, we interrogate two new modifications in inverse Weierstrass iterative method for estimating all roots of non-linear equation simultaneously. These modifications enables us to accelerate the convergence order of inverse Weierstrass method from 2 to 3. Convergence analysis proves that the orders of convergence of the two newly constructed inverse methods are 3. Using computer algebra system Mathematica, we find the lower bound of the convergence order and verify it theoretically. Dynamical planes of the inverse simultaneous methods and classical iterative methods are generated using MATLAB (R2011b), to present the global convergence properties of inverse simultaneous iterative methods as compared to classical methods. Some non-linear models are taken from Physics, Chemistry and engineering to demonstrate the performance and efficiency of the newly constructed methods. Computational CPU time, and residual graphs of the methods are provided to present the dominance behavior of our newly constructed methods as compared to existing inverse and classical simultaneous iterative methods in the literature.

Automated summary

This research article investigates two new modifications to the inverse Weierstrass iterative method, aiming to accelerate the convergence order to 3. Using computational algebra system and MATLAB, the efficiency and performance of the newly constructed methods have been validated and proven to be superior to existing inverse and classical simultaneous iterative methods.