Semilocal convergence by using recurrence relations for a fifth-order method in Banach spaces

• Alicia Cordero ; Miguel Angel Hernández Verón ^[1] ; Natalia Romero Álvarez ^[1] ; Juan Ramón Torregrosa Sánchez ^[2]
  1. [1] Universidad de La Rioja

     Universidad de La Rioja

     Logroño, España

     
  2. [2] Universidad Politécnica de Valencia

     Universidad Politécnica de Valencia

     Valencia, España

     
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 273, Nº 1, 2015, págs. 205-213
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • In this paper, a semilocal convergence result in Banach spaces of an efficient fifth-order method is analyzed. Recurrence relations are used in order to prove this convergence, and some a priori error bounds are found. This scheme is finally used to estimate the solution of an integral equation and so, the theoretical results are numerically checked. We use this example to show the better efficiency of the current method compared with other existing ones, including Newton�s scheme.