Generalization of the bisection method and its applications in nonlinear equations

Abstract

The aim of the current work is to generalize the well-known bisection method using quantum calculus approach. The results for different values of quantum parameter q are analyzed, and the rate of convergence for each q∈ (0 , 1) is also determined. Some physical problems in engineering are resolved using the QBM technique for various values of the quantum parameter q up to three iterations to examine the validity of the method. Furthermore, it is proven that QBM is always convergent and that for each interval there exists q∈ (0 , 1) for which the first approximation of root coincides with the precise solution of the problem.