On the convergence of Newton-like MS method with dynamics and applications

Manoj K. Singh ^[1] ; B. R. Singh ^[1] ; Deepak Kumar Mishra ^[1]
1. [1] College of Technology, Sardar Vallabhbhai Patel University of Agriculture and Technology, Meerut
Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol. 80, Nº. 4, 2023, págs. 663-686
Idioma: inglés
DOI: 10.1007/s40324-022-00311-3
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Resumen
- The motive of this work is to introduce and investigate the benefits and defects of a new three-step Newton-like iterative method to solve nonlinear operator equations in Banach space. We discussed the local and more importantly semi-local convergence analysis for the proposed method. Some numerical examples along with one boundary value problem are given to show that the speed of convergence of the proposed iterative method is faster than the modified Newton’s method and Sahu et al. method. Lastly, the dynamical analysis confirms the theoretical and numerical results, but reveals some drawback of this type of Newton-like S method.