A New Root–Finding Algorithm Using Exponential Series

• Published in: Ural mathematical journal Vol. 5; no. 1; pp. 83 - 90
• Main Author: Thota, Srinivasarao
• Format: Journal Article
• Language: English
• Published: Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin 2019
• Subjects: Algebraic equations, Transcendental equations, Exponential series, Secant method
• ISSN: 2414-3952; 2414-3952
• DOI: 10.15826/umj.2019.1.008

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.