Extended domain for fifth convergence order schemes

• Autores: Ioannis K. Argyros, Santhosh George
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 23, Nº. 1, 2021, págs. 97-108
• Idioma: inglés
• DOI: 10.4067/S0719-06462021000100097
• Enlaces
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• Resumen
  • español

    Resumen Entregamos un análisis local y uno semi-local de un esquema de quinto orden de convergencia que involucra operadores con valores en un espacio de Banach para resolver ecuaciones nolineales. El dominio de convergencia es extendido resultando en un análisis de convergencia más fino para ambos tipos. Esto se logra ubicando un dominio más pequeño incluido en el dominio antiguo, entregando funciones de tipo Lipschitz más ajustadas. Estas extensiones se obtienen sin hipótesis adicionales. Se usan ejemplos numéricos para verificar los criterios de convergencia y también para mostrar que nuestros resultados son superiores a otros anteriores. Nuestra idea se puede utilizar para extender otros esquemas usando inversos de manera similar.

  • English

    Abstract We provide a local as well as a semi-local analysis of a fifth convergence order scheme involving operators valued on Banach space for solving nonlinear equations. The convergence domain is extended resulting a finer convergence analysis for both types. This is achieved by locating a smaller domain included in the older domain leading this way to tighter Lipschitz type functions. These extensions are obtained without additional hypotheses. Numerical examples are used to test the convergence criteria and also to show the superiority for our results over earlier ones. Our idea can be utilized to extend other schemes using inverses in a similar way.

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