Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

On Efficient Iterative Numerical Methods for Simultaneous Determination of all Roots of Non-Linear Function

Version 1 : Received: 26 February 2020 / Approved: 27 February 2020 / Online: 27 February 2020 (16:02:39 CET)

How to cite: Shams, M.; Mir, N.; Rafiq, N. On Efficient Iterative Numerical Methods for Simultaneous Determination of all Roots of Non-Linear Function. Preprints 2020, 2020020410 (doi: 10.20944/preprints202002.0410.v1). Shams, M.; Mir, N.; Rafiq, N. On Efficient Iterative Numerical Methods for Simultaneous Determination of all Roots of Non-Linear Function. Preprints 2020, 2020020410 (doi: 10.20944/preprints202002.0410.v1).

Abstract

We construct a family of two-step optimal fourth order iterative methods for finding single root of non-linear equations. We generalize these methods to simultaneous iterative methods for determining all the distinct as well as multiple roots of single variable non-linear equations. Convergence analysis is present for both cases to show that the order of convergence is four in case of single root finding method and is twelve for simultaneous determination of all roots of non-linear equation. The computational cost, Basin of attraction, efficiency, log of residual and numerical test examples shows, the newly constructed methods are more efficient as compared to the existing methods in literature.

Subject Areas

Single roots; Distinct roots; Multiple roots; Optimal order; Non-Linear equation; Iterative methods; Simultaneous Methods; Basin of attraction; Computational Efficiency

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