Numerical Simulation of Nonlinear Equations by using Modified Newton Raphson Technique

Abstract

Non-linear equations are a significant number of complicated issues in mathematics and related subjects that must be solved. The Newton method and its preliminary variations are among the most basic, yet insufficiently effective, methods for resolving non-linear equations. To solve non-linear equations efficiently, a method's desirable feature is to find root with fewer iterations, minimum error (usually less than precision limit), which is typically less than the precision limit. In, this work, we present two approaches (Proposed techniques I and II) for solving non-linear equations by modifying Newton Raphson's technique using first derivative's forward and central difference approximations. Two examples are used to compare performance of the suggested techniques with the existing technique (Secant technique). Finding roots of nonlinear equations under consideration required fewer iterations and a lower absolute relative approximate error while using proposed method II, which performed better than both existing methods (the Secant technique and suggested method I). The suggested approaches I and II were determined to be appropriate substitutes for solving nonlinear equations.