Local Convergence for an Improved Jarratt-type Method in Banach Space

• Autores: Ioannis K. Argyros, Daniel González Sánchez
• Localización: IJIMAI, ISSN-e 1989-1660, Vol. 3, Nº. 4, 2015, págs. 20-25
• Idioma: inglés
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• Resumen

  • We present a local convergence analysis for an improved Jarratt-type methods of order at least five to approximate a solution of a nonlinear equation in a Banach space setting. The convergence ball and error estimates are given using hypotheses up to the first Fre´chet derivative in contrast to earlier studies using hypotheses up to the third Fre´chet derivative. Numerical examples are also provided in this study, where the older hypotheses are not satisfied to solve equations but the new hypotheses are satisfied.