Generalization of the bisection method and its applications in nonlinear equations

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