Convergence, Dynamics and Real-World Applications of C-H Method for Multiple Zeros of Analytic Functions

Authors

  • Rajat Subhra Das Department of Mathematics, Dr. L.K.V.D. College (affiliated to L. N. Mithila University, Darbhanga), Tajpur, Samastipur 848130, Bihar, India
  • Abhimanyu Kumar Department of Mathematics, L.N. Mithila University, Darbhanga 847233, Bihar, India
  • Neha Varma Department of Mathematics, L.N. Mithila University, Darbhanga 847233, Bihar, India

DOI:

https://doi.org/10.26713/cma.v17i1.3434

Keywords:

Chebyshev method, Halley method, Multiple zeros, Analytic functions, Error estimates, Local convergence, Basins of attraction

Abstract

In this study, we focus on the local convergence properties of the C-H combined mean technique applied to analytic functions having simple and multiple zeros. C-H combined mean technique is essentially the average of the two well-known approaches, the Halley’s method and the Chebyshev’s method. As an outcome, we provide a convergence theorem that guarantees the Q-cubic convergence of the C-H combined mean technique from the very beginning by giving precise domains of starting points together with error estimates. Furthermore, real-life applications demonstrate the robustness and efficiency of the C-H combined mean technique.

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Author Biographies

  • Abhimanyu Kumar, Department of Mathematics, L.N. Mithila University, Darbhanga 847233, Bihar, India

     

     
  • Neha Varma, Department of Mathematics, L.N. Mithila University, Darbhanga 847233, Bihar, India

     

     

Published

30-03-2026

Issue

Vol. 17 No. 1 (2026)

Section

Research Article

License

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How to Cite

Das, R. S., Kumar, A., & Varma, N. (2026). Convergence, Dynamics and Real-World Applications of C-H Method for Multiple Zeros of Analytic Functions. Communications in Mathematics and Applications, 17(1), 79-89. https://doi.org/10.26713/cma.v17i1.3434