Application Of Multipoint Secant-Type Method ForFinding Roots 0f Nonlinear Equations

R.  Thukral

doi:10.24297/jam.v23i.9588

Authors

R. Thukral Padé Research Centre, 39 Deanswood Hill, Leeds, West Yorkshire, LS17 5JS, England

DOI:

https://doi.org/10.24297/jam.v23i.9588

Keywords:

Order of convergence, Root-finding, Nonlinear algebraic equations, Simple root, Secant-type methods

Abstract

In this paper, we introduce a family of p_k-order iterative schemes for finding the simple root of a nonlinear algebraic equation of the function fx=0 by using the divided difference approximation. The proposed method uses one evaluation of the function per iteration and can achieve convergence order p_k. The error equation and asymptotic convergence constant are proved theoretically and numerically. Numerical examples are included to demonstrate the exceptional convergence speed of the proposed method and thus verify the theoretical results

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References

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