Modified Bracketing Iterative Method for Solving Nonlinear Equations

Abstract

Non-linear equations, depicted as curves in numerous everyday situations, have long piqued the curiosity of researchers and engineers due to their frequent occurrence in practical problems. Despite attempts to tackle these equations both analytically and numerically, analytical methods often fall short when the equation's degree exceeds five, prompting the adoption of numerical approaches to yield approximate solutions. Consequently, this study places emphasis on segmenting intervals into smaller sub-intervals, with a particular focus on employing the Regula-Falsi method to integrate these segmented intervals, thereby enhancing its convergence rate. Furthermore, by utilizing the Regula-Falsi formula for interval segmentation, the number of iterations and computational time required are minimized. Additionally, the effectiveness of the proposed method is verified through numerical experiments involving various equation types, including algebraic, trigonometric, exponential, logarithmic, and transcendental equations, comparing the outcomes with established methods. The findings demonstrate that the proposed algorithm not only efficiently segments intervals but also enhances accuracy and reduces errors when these segmented intervals are utilized in conventional bracketing methods.