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

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Chennai, 601103, India

    Sunil Kumar

  2. Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal, 148106, Punjab, India

    Deepak Kumar

  3. Department of Secondary Education, AMSSS Uklana (Hisar), Uklana, 125113, Haryana, India

    Rakesh Kumar

Authors
  1. Sunil Kumar
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  2. Deepak Kumar
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  3. Rakesh Kumar
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Correspondence to Sunil Kumar.

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Kumar, S., Kumar, D. & Kumar, R. Development of cubically convergent iterative derivative free methods for computing multiple roots. SeMA 80, 415–423 (2023). https://doi.org/10.1007/s40324-022-00300-6

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