The College of Education for Pure Sciences, Department of Mathematics, University of Basra, discussed a master’s thesis on efficient iterative methods based on Bernstein’s polynomial and modified homotopy perturbation theory to solve nonlinear equations.
The thesis presented by the researcher (Hoda Jabbar Saeed) included many new iterative methods for solving nonlinear equations using different numerical techniques, including quadratic formulas and the modified homotopy perturbation method. The convergence of the new iterative methods was demonstrated. The efficiency guide for the proposed iterative methods was also discussed with a comparison with some other related iterative methods. Several numerical examples were presented to demonstrate the effectiveness and performance of the new iterative methods. also,
The study showed that these iterative methods obtained using different numerical techniques include some known iterative methods as special cases. The computational results also indicate that iterative methods converge faster, and require fewer iterations compared to other iterative methods. This is in agreement with the theoretical results obtained regarding the affinity rank and the proficiency index.
