New Trigonometrically Method for Solving Non-Linear Transcendental Equations

Abstract: The transcendental equations' non-zero positive real roots can be found using a new approach presented in this research. The proposed approach is based on the union of the Newton-Raphson method and the inverse tan(x) function. To ensure the method's applicability, it is implemented in MATLAB and applied to various issues. The suggested approach is evaluated on a variety of numerical instances, the results show that our approaches are superior and more efficient than widely used methods. For both the new proposed method and the currently accessible existing methods, error calculations have been made. When compared to well-known procedures, the mistakes were quickly minimised, and the genuine root was discovered in fewer repetitions. The proposed method's convergence is studied, and it is demonstrated that it reduces to the quadratic convergent Newton-Raphson method. This method will also assist in the production of a non-zero real root of a specified nonlinear equation in the commercial software (transcendental, algebraic, and exponential).