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Proposed Section Methods to Find Root of the Single Variable Non-Linear Algebraic and Transcendental Equations

The main purpose of numerical analysis is to develop a numerical algorithm to find approximate values. The main aim of this paper is to present Proposed Section Method-I and Proposed Section Method-II (Proposed Section Methods). These method makes some slight difference in well-known bisection method to solve single variable nonlinear equation. In well-known Bisection Method, the interval in which the root of the equation lies is bisected using Arithmetic Mean (AM). These Proposed Section Method splits the interval using Geometric Mean (GM) and Harmonic Mean (HM). These method gives the roots of the equation which are closed to the root given by well-known Bisection Method. In order to analyze the results some examples related with algebraic and transcendental functions are considered. It was concluded that if the root of the single variable non-linear equation exists by all these methods then the solutions are very close to each other.