Development of cubically convergent iterative derivative free methods for computing multiple roots

• Sunil Kumar ^[2] ; Deepak Kumar ^[1] ; Rakesh Kumar ^[3]
  1. [1] Sant Longowal Institute of Engineering and Technology

     Sant Longowal Institute of Engineering and Technology

     India

     
  2. [2] Department of Mathematics, Amrita School of Engineering
  3. [3] Department of Secondary Education, AMSSS Uklana (Hisar)

  Mostrar afiliaciones +
• Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol. 80, Nº. 3, 2023, págs. 415-423
• Idioma: inglés
• DOI: 10.1007/s40324-022-00300-6
• Enlaces
  • Texto Completo Ejemplar
• Resumen

  • This research article is dedicated to solving multiple roots of real life problems. In the literature, there are numerous higher-order multiple root algorithms with derivative. But, derivative-free algorithms for multiple roots, on the other hand, are extremely rare. As a result of this, we describe a family of third-order derivative-free algorithms for calculating multiple roots that only require three function evaluations each iteration. The application of new algorithms is validated on Shokley diode and electric circuit problem, Isothermal continuous stirred tank reactor problem, Van der Waals problem and Planck law radiation problem. The presented iterative algorithms are good rivals to the existing algorithms, according to numerical results.