Development and Application of the DMS Iterative Method Having Third Order of Convergence

In the present work, we suggest a fixed-point-based iterative method (the DMS iterative method) to attain numerical solutions of nonlinear equations of one variable arising in the real-world phenomena. We analytically obtain the order of convergence and the efficiency index of the developed (DMS) method which are 3 and 1.4422, respectively, both of which are higher than the famous Newton–Raphson (the N-R) method. The efficiency index of our method turns out to be the optimum value for one-point iterative methods for which number of function evaluations and order of convergence are same. Two examples from the physical sciences have been taken which reflect that the method used is solution-oriented and leads to the real root in the fewer number of iterations as compared to the Newton–Raphson method, which also complies with the analytical denouement. Graphs for both of the problems have been included which depict the same.