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

Abstract

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.

Implementation of Numerical Integration Simpson 3/8 Rule to Develop a Numerical Simpson Iterative Method for Solving Non-Linear Equations

“…The developed technique has quadratic converge. This paper reflects the idea and more better results from the work of the authors of [7][8]. Examples are given to show that the proposed iterative method is better than compared methods.…”

“…Similarly, this paper has suggested a numerical iteration method for solving nonlinear equations. The idea of the proposed iteration method comes from [7] and [8] given by…”

“…In the same way, the proposed numerical iteration method depends on the simpson 3/8th rule and numerical techniques. The developed numerical iteration method was assessed against the newton raphson method and the trapezoidal method [8][9]. The numerical results demonstrate that the proposed method is better than the existing second order iterated methods in terms of the accuracy of the iterations in solving nonlinear equations.…”