An Iterative Method for Solving Nonlinear Equations Based on the Inverse Hyperbolic Sine Function

RAGHURAMBHATTAR K; C Balarama Krishna; B. Ravindar; G. Mahesh

doi:10.5269/bspm.82343

Autores

RAGHURAM KORUKONDA BHATTAR SR University
C Balarama Krishna SR University, Warangal, Telangana, India https://orcid.org/0000-0002-1554-0945
B. Ravindar SR University, Warangal, Telangana, India https://orcid.org/0000-0001-8203-5044
G. Mahesh Keshav Memorial Institute of Technology, Narayanaguda, Hyderabad https://orcid.org/0000-0002-4075-8751

DOI:

https://doi.org/10.5269/bspm.82343

Resumo

An iterative method for solving single-variable nonlinear equations based on the inverse hyperbolic sine (asinh) function is proposed. The method reformulates the original nonlinear equation into an equivalent iterative scheme that incorporates the analytical properties of the asinh function to enhance numerical stability and convergence behavior. A rigorous theoretical analysis establishes that the proposed method achieves quadratic convergence under suitable assumptions. To evaluate its performance, several numerical experiments are conducted on representative algebraic, transcendental, and trigonometric test problems. The numerical results are compared with classical root-finding techniques, including the Bisection method, Regula Falsi method, Newton–Raphson method, and Steffensen method. The comparisons demonstrate that the proposed asinh-based method provides higher accuracy, faster convergence, and improved robustness, particularly for poor initial approximations. All computations are implemented using Python to ensure numerical reliability and reproducibility.

Biografia do Autor

C Balarama Krishna, SR University, Warangal, Telangana, India

C Balarama Krishna is affiliated with the Department of Mathematics, School of Computer Science & Artificial Intelligence, SR University, Warangal, Telangana, India. His research interests include numerical analysis, computational mathematics, and root-finding algorithms.
B. Ravindar, SR University, Warangal, Telangana, India

B. Ravindar is affiliated with the Department of Mathematics, School of Computer Science & Artificial Intelligence, SR University, Warangal, Telangana, India. His research interests include numerical methods, nonlinear analysis, computational mathematics, and iterative techniques for solving nonlinear equations.
G. Mahesh, Keshav Memorial Institute of Technology, Narayanaguda, Hyderabad

G. Mahesh is affiliated with the Department of Humanities and Sciences, Keshav Memorial Institute of Technology, Narayanaguda, Hyderabad, Telangana, India. His research interests include numerical analysis, nonlinear equations, root-finding algorithms, and computational mathematics.

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