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

Abstract

This research paper has developed a numerical iterative method by using Simpson 3/8 rule for solving non-linear equations, which equations are studied in different sciences and engineering fields. 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. Our developed method is compared with the Newton Raphson method and the Trapezoidal method. C++/MATLAB was used to compute the numerical results. It can be observed from the results that the simpson iterative method is better than the Newton Raphson method, and the Trapezoidal method in terms of iteration and accuracy perception.