An integrated approach of the numerical simulation of nonlinear equations by modified bisection and Regula Falsi method

This paper presents an integrated approach to the numerical simulation of nonlinear algebraic and transcendental equations using modified versions of the Bisection and Regula Falsi methods. The study aims to improve the efficiency and accuracy of root-finding algorithms for complex non-linear equations. We introduce modifications to the classical Bisection and Regula Falsi methods and compare their performance against traditional approaches. The research includes a comprehensive analysis of convergence rates, error margins, and computational complexity. Our findings demonstrate that the modified methods offer significant improvements in terms of speed and precision for a wide range of non-linear equations. The paper includes detailed tables presenting comparative results and discusses the implications of these findings for various fields of applied mathematics and engineering.