### A NEW ROOT–FINDING ALGORITHM USING EXPONENTIAL SERIES

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

#### Abstract

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.

#### Keywords

Algebraic equations, Transcendental equations, Exponential series, Secant method

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