A Numerical approach to Solve Nonlinear Univariate Equation Using Inverse Hyperbolic Tangent Function

Résumé

The fundamental idea behind the proposed method is to use the inverse hyperbolic tangent func
tion, which offers a computationally efficient and mathematically efficient root-finding framework. MATLAB
is used widely to implement the approach, guaranteeing a useful and repeatable computing environment. The
proposed method is tested on many common benchmark problems found in mathematical modeling and engi
neering to check how well it works, how accurate it is, and how strong it remains under different conditions.
These problems are carefully selected to test the method at different levels of nonlinearity and complexity. A
detailed set of numerical experiments is carried out to evaluate how well the proposed method works. The
results clearly show that the proposed method consistently performs somewhat better than several well-known
root-finding techniques in both convergence speed and computational accuracy. A detailed error analysis,
showing the accuracy and stability of the proposed method in different situations, further confirms its effec
tiveness and reliability. In addition, a detailed theoretical analysis is carried out to show that the proposed
method exhibits quadratic convergence, which means the error decreases significantly with each iteration. Due
to its fast convergence rate, the method is capable of providing highly accurate results using fewer iterations,
thereby reducing the overall computational effort and time required for the solution.