An Efficient Family of Optimal Eighth-Order Multiple Root Finders

Fiza Zafar, Alicia Cordero and Juan R. Torregrosa
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Fiza Zafar: Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60800, Pakistan
Alicia Cordero: Instituto de Matemáticas Multidisciplinar, Universitat Politènica de València, 46022 València, Spain
Juan R. Torregrosa: Instituto de Matemáticas Multidisciplinar, Universitat Politènica de València, 46022 València, Spain

Mathematics, 2018, vol. 6, issue 12, 1-16

Abstract: Finding a repeated zero for a nonlinear equation f ( x ) = 0 , f : I ⊆ R → R has always been of much interest and attention due to its wide applications in many fields of science and engineering. Modified Newton’s method is usually applied to solve this kind of problems. Keeping in view that very few optimal higher-order convergent methods exist for multiple roots, we present a new family of optimal eighth-order convergent iterative methods for multiple roots with known multiplicity involving a multivariate weight function. The numerical performance of the proposed methods is analyzed extensively along with the basins of attractions. Real life models from life science, engineering, and physics are considered for the sake of comparison. The numerical experiments and dynamical analysis show that our proposed methods are efficient for determining multiple roots of nonlinear equations.

Keywords: nonlinear equations; multiple zeros; optimal iterative methods; higher order of convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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