An Adaptive Algorithm for Roots of Non-Linear Equations

Optimization problems lead to non-linear equations fordetermining their roots efficiently.Finding the roots of a non-linear equation is a fundamental problem in diverse fields.Numerical iterative techniques become necessary when analytic solution is not available.Recently, some attempts Adapt1 combination of Bisection and Regula Falsi; Adapt2 a blend of Trisection and Regula Falsi; and Adapt3 a composite of Trisection and Newton-Raphson methods emerged to design adaptive algorithms.In this paper, we design a new heuristic algorithm Adapt4 which is an intuitive approach.The new algorithmAdapt4 promises to be more efficient than the existing adaptive algorithms.The new adapted algorithm is a blend of BT section algorithm and Regula Falsi algorithm.The algorithm Adapt4 reduces the number of iterations and the computation time of each iteration.The implementation results validate that the new algorithmAdapt4, surpasses theefficiency of existing such algorithms Adapt1, Adapt2, and Adapt3 algorithms.This paper contributes an essential adaptive algorithm for finding roots of frequent engineering equations.