An Improved Secant Algorithm of Variable Order to Solve Nonlinear Equations Based on the Disassociation of Numerical Approximations and Iterative Progression
- Christian Vanhille
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).
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- DOI:10.5539/jmr.v12n6p50
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