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An Improved Secant Algorithm of Variable Order to Solve Nonlinear Equations Based on the Disassociation of Numerical Approximations and Iterative Progression

Christian Vanhille

Journal of Mathematics Research, 2020, vol. 12, issue 6, 50

Abstract: We propose an iterative method to evaluate the roots of nonlinear equations. This Secant-based technique approximates the derivatives of the function numerically through a constant discretization step h disassociated from the iterative progression. The algorithm is developed, implemented, and tested. Its order of convergence is found to be h-dependent. The results obtained corroborate the theoretical deductions and evidence its excellent behavior. For infinitesimal h-values, the algorithm accelerates the convergence of the Secant method to order 2 (the one of the Newton-Raphson method) with no need for analytic expression of derivatives (the advantage of the Secant method).

JEL-codes: R00 Z0 (search for similar items in EconPapers)
Date: 2020
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Handle: RePEc:ibn:jmrjnl:v:12:y:2020:i:6:p:50