Abstract:- The paper is about Newton Raphson Method and Secant Method, the secant method and the newton Raphson method is very effective numerical procedure used for solving non - linear equations of the form f(x)=0. which is all-inclusive to solve the non-square and non-linear problem. It represents a new approach of calculation using nonlinear equation, this paper also discusses the difference between both the methods also the advantages and disadvantages the derivation Newton Raphson formula, algorithm, use and drawbacks of Newton Raphson Method have also been discussed. Secant method is derived via linear Interpolation we provides its error in closed form and analyze its order of Convergence is greater than that of these cant method, and it increases as k Increases.

Keywords: Convergence, non-linear problems.

| DOI: 10.17148/IJIREEICE.2022.101106