# A new trigonometrical method for solving non-linear transcendental equations

Volume 25, Issue 2, pp 176--181
Publication Date: May 27, 2021 Submission Date: February 16, 2021 Revision Date: April 10, 2021 Accteptance Date: May 01, 2021
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### Authors

K. Venkateshwarlu - Department of Freshman Engineering, Geethanjali College of Engineering and Technology, Cheeryal(V), Keesara(M), Medchal Dist. Telangana, , India. V. S. Triveni - Department of Freshman Engineering, Geethanjali College of Engineering and Technology, Cheeryal(V), Keesara(M), Medchal Dist. Telangana, India. G. Mahesh - Department of Freshman Engineering, Geethanjali College of Engineering and Technology, Cheeryal(V), Keesara(M), Medchal Dist. Telangana, India. G. Swapna - Department of Humanities and Sciences, Geethanjali College of Pharmacy, Cheeryal(V), Keesara(M), Medchal Dist. Telangana, India.

### Abstract

This paper presents a new algorithm to find a non-zero positive real root of the transcendental equations. The proposed method is based on the combination of the inverse $\tan(x)$ function and the Newton-Raphson method. Implementation of the proposed method in MATLAB is applied to different problems to ensure the methodâ€™s applicability. The proposed method is tested on number of numerical examples and results indicate that our methods are better and more effective as compared to well-known methods. Error calculation has been done for available existing methods and the new proposed method. The errors have been reduced rapidly and obtained the real root in less number of iterations as compared to renowned methods. Certain numerical examples are presented in this paper to show the effectiveness of the proposed method. The Convergence of the proposed method is discussed and shown that the method reduces to Newton-Raphson method that is quadratic convergent. This approach will also help to produce a non-zero real root of a given non-linear equations (transcendental, algebraic, and exponential) in the commercial package.

### Share and Cite

##### ISRP Style

K. Venkateshwarlu, V. S. Triveni, G. Mahesh, G. Swapna, A new trigonometrical method for solving non-linear transcendental equations, Journal of Mathematics and Computer Science, 25 (2022), no. 2, 176--181

##### AMA Style

Venkateshwarlu K., Triveni V. S., Mahesh G., Swapna G., A new trigonometrical method for solving non-linear transcendental equations. J Math Comput SCI-JM. (2022); 25(2):176--181

##### Chicago/Turabian Style

Venkateshwarlu, K., Triveni, V. S., Mahesh, G., Swapna, G.. "A new trigonometrical method for solving non-linear transcendental equations." Journal of Mathematics and Computer Science, 25, no. 2 (2022): 176--181

### Keywords

• Nonlinear equation
• iteration method
• transcendental equations

•  65H04
•  65H05

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