Abstract
AbstractThe aim of the current work is to generalize the well-known bisection method using quantum calculus approach. The results for different values of quantum parameterqare analyzed, and the rate of convergence for each$q\in (0,1)$q∈(0,1)is also determined. Some physical problems in engineering are resolved using the QBM technique for various values of the quantum parameterqup 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$q\in (0,1)$q∈(0,1)for which the first approximation of root coincides with the precise solution of the problem.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
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