Srinivasarao Thota     (Department of Applied Mathematics, School of Applied Natural Sciences, Adama Science and Technology University, Post Box No. 1888, Adama, Ethiopia)


In this paper, we present a new root-finding algorithm to compute a non-zero real root of the transcendental equations using exponential series. Indeed, the new proposed algorithm is based on the exponential series and in which Secant method is special case. The proposed algorithm produces better approximate root than bisection method, regula-falsi method, Newton-Raphson method and secant method. The implementation of the proposed algorithm in Matlab and Maple also presented. Certain numerical examples are presented to validate the efficiency of the proposed algorithm. This algorithm will help to implement in the commercial package for finding a real root of a given transcendental equation.


Algebraic equations, Transcendental equations, Exponential series, Secant method

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Datta B.N. Lecture Notes on Numerical Solution of Root–Finding Problems. 2012. URL: http://www.math.niu.edu/~dattab/math435.2009/ROOT-FINDING.pdf

Chen J. New modified regula falsi method for nonlinear equations. Appl. Math. Comput., 2007. Vol. 184, No. 2. P. 965–971. DOI: 10.1016/j.amc.2006.05.203

Noor M.A., Noor K.I., Khan W.A., Ahmad F. On iterative methods for nonlinear equations. Appl. Math. Comput., 2006. Vol. 183, No. 1. P. 128–133. DOI: 10.1016/j.amc.2006.05.054

Noor M.A., Ahmad F. Numerical comparison of iterative methods for solving nonlinear equations. Appl. Math. Comput., 2006. Vol. 180, No. 1. P. 167–172. DOI: 10.1016/j.amc.2005.11.151

Ehiwario J.C., Aghamie S.O. Comparative study of bisection, Newton-Raphson and secant methods of root–finding problems. IOSR J. of Engineering, 2014. Vol. 4, No. 4. P. 1–7.

Hussain S., Srivastav V.K., Thota S. Assessment of interpolation methods for solving the real life problem. Int. J. Math. Sci. Appl., 2015. Vol. 5, No. 1. P. 91–95. http://ijmsa.yolasite.com/resources/12.pdf

Sagraloff M., Mehlhorn K. Computing Real Roots of Real Polynomials. 2013. arXiv: 1308.4088v2 [cs.SC].

Thota S., Srivastav V.K. Quadratically convergent algorithm for computing real root of non-linear transcendental equations. BMC Research Notes, 2018. Vol. 11, art. no. 909. DOI: 10.1186/s13104-018-4008-z

Thota S., Srivastav V.K. Interpolation based hybrid algorithm for computing real root of non-linear transcendental functions. Int. J. Math. Comput. Research, 2014. Vol. 2, No. 11, P. 729–735. URL: http://ijmcr.in/index.php/ijmcr/article/view/182/181

Abbasbandy S., Liao S. A new modification of false position method based on homotopy analysis method. Appl. Math. Mech., 2008. Vol. 29, No. 2. P. 223–228. DOI: 10.1007/s10483-008-0209-z

Srivastav V.K., Thota S., Kumar M. A new trigonometrical algorithm for computing real root of non-linear transcendental equations. Int. J. Appl. Comput. Math., 2019. Vol. 5, art. no. 44. DOI: 10.1007/s40819-019-0600-8

DOI: http://dx.doi.org/10.15826/umj.2019.1.008

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