Quadratically convergent algorithm for computing real root of non‑linear transcendental equations (original) (raw)
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Ural Mathematical Journal, 2023
The objective of this paper is to propose two new hybrid root finding algorithms for solving transcendental equations. The proposed algorithms are based on the well-known root finding methods namely the Halley's method, regula-falsi method and exponential method. We show using numerical examples that the proposed algorithms converge faster than other related methods. The first hybrid algorithm consists of regula-falsi method and exponential method (RF-EXP). In the second hybrid algorithm, we use regula-falsi method and Halley's method (RF-Halley). Several numerical examples are presented to illustrate the proposed algorithms, and comparison of these algorithms with other existing methods are presented to show the efficiency and accuracy. The implementation of the proposed algorithms is presented in Microsoft Excel (MS Excel) and the mathematical software tool Maple.
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Southeast Asian Journal of Sciences, 2019
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Comparative Study of Bisection and Newton-Rhapson Methods of Root-Finding Problems
mekele
This paper presents two numerical techniques of root-finding problems of a non-linear equations with the assumption that a solution exists, the rate of convergence of Bisection method and Newton-Rhapson method of root-finding is also been discussed. The software package , MATLAB 7.6 was used to find the root of the function, f (x) = cosx − x * exp(x) on a close interval [0, 1] using the Bisection method and Newton's method the result was compared. It was observed that the Bisection method converges at the 14 th iteration while Newton methods converge to the exact root of 0.5718 with error 0.0000 at the 2 nd iteration respectively. It was then concluded that of the two methods considered, Newton's method is the most effective scheme. This is in line with the result in our Ref.[9].
New Trigonometrically Method for Solving Non-Linear Transcendental Equations
International Journal for Research in Applied Science & Engineering Technology (IJRASET), 2022
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).