University of KwaZulu-Natal, School of Mathematics, Statistics and Computer Sciences, Private Bag X01, 3209 Scottsville, Pietermaritzburg, South Africa
University of KwaZulu-Natal, School of Mathematics, Statistics and Computer Sciences, Private Bag X01, 3209 Scottsville, Pietermaritzburg, South Africa; University of Swaziland, Mathematics Department, Private Bag 4, M201 Kwaluseni, Swaziland
The main motivation of this study is to propose an optimal scheme with an inverse interpolatory rational function error corrector in a general way that can be applied to any existing optimal multi-point fourth-order iterative scheme whose first sub step employs Newton’s method to further produce optimal eighth-order iterative schemes. In addition, we also discussed the theoretical and computational properties of our scheme. Variety of concrete numerical experiments and basins of attraction are extensively treated to confirm the theoretical development.
Kim, Y. I., Behl, R., & Motsa, S. S. (2017). An Optimal Family of Eighth-Order Iterative Methods with an Inverse Interpolatory Rational Function Error Corrector for Nonlinear Equations. Mathematical Modelling and Analysis, 22(3), 321-336. https://doi.org/10.3846/13926292.2017.1309585
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