Newton-Raphson Method and Regular- Falsi Method For Solving The Roots

Abstract: For solving nonlinear equations of the form f(x) = 0, two highly efficient numerical techniques are used: the regula falsi, Newton-Raphson methods. They are obtained using techniques for linear interpolation. Their studies can be completed by utilising Newton's interpolation formula, divided differences, and interpolation theory. We integrate these studies. The information should also be a helpful exercise or example for the usage of split differences and polynomial interpolation in introductory courses in numerical analysis. In this text we have compared the two methods and their functions.