Comparison of Proposed and Existing Fourth Order Schemes for Solving Non-linear Equations

This paper, investigates the comparison of the convergence behavior of the proposed scheme and existing schemes in literature. While all schemes having fourth-order convergence and derivative-free nature. Numerical approximation demonstrates that the proposed schemes are able to attain up to better accuracy than some classical methods, while still significantly reducing the total number of iterations. This study has considered some nonlinear equations (transcendental, algebraic and exponential) along with two complex mathematical models. For better analysis graphical representation of numerical methods for finding the real root of nonlinear equations with varying parameters has been included. The proposed scheme is better in reducing error rapidly, hence converges faster as compared to the existing schemes.