An optimal 8th order Newton’s-type method with basin of attraction

• Autores: Manoj Kumar Singh, Ioannis Karatzas, Arvind K. Singh
• Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol. 79, Nº. 4, 2022, págs. 631-645
• Idioma: inglés
• DOI: 10.1007/s40324-021-00262-1
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• Resumen

  • The goal of the present work is to obtain an eighth order optimal Newton like method to solve non-linear algebraic equations. We also examine the dynamics of the proposed method. It is an optimal eighth order consistent with Kung–Traub conjecture with efficiency index 1.682. We have tested the proposed method using several numerical examples and also discussed the basin of attraction related to some numerical examples.