Optimizing Computational Efficiency in Numerical Methods: A Comparative Analysis of Algorithms and Implementation in MATLAB

This research investigates and compares the overall performance of different numerical methods, and focuses on their accuracy, what will be the convergence rate, and the computational cost of each algorithm. A thorough analysis of different algorithms and optimization techniques will serve to improve the computational effectiveness of MATLAB and other programs that are used. This will focus on comparing the Newton Raphson Method, and how well it works in solving an equation through the use of Python IDLE Program and MATLAB Software. Through a comparative analysis, this study aims to identify the applicability of the algorithms that are used. This work investigates new approaches to error reduction, addressing problems related to accuracy and numerical stability. Through comparison, the benefits, drawbacks, and suitability of different numerical techniques are assessed. The ultimate aim of this work is to offer researchers practical guidance on the selection and optimization of numerical methods in MATLAB. More complex numerical simulations in scientific and engineering applications will be possible with improved computational efficiency and reliability, which are anticipated outcomes. The researchers conclude that regardless of the programming software being used in an equation, the results will remain the same but with a minor discrepancy.