USING NEWTON-RAPHSON'S METHOD TO CALCULATE THE APPROXIMATE SOLUTIONS OF THE VARIABLES OF A NON-LINEAR MODEL EQUATION FOR CHOLERA DISEASE AFTER SOME ITERATIONS.

Abstract

To solve a nonlinear equation, the Newton-Raphson technique employs the idea of iterative approximation. Every iteration is used to improve the original guess value for the answer and bring it closer to the real solution. By calculating the derivative of the nonlinear equation at that point, the iterations are based on linearization around the current guess. The guess is updated using the linear approximation by deducting the linearization's value from the prior guess. Until the precise answer is found, this procedure is repeated. In order to solve the non-linear equations, an iterative technique is a mathematical procedure that is utilized as a starting value to build a series of improving approximation solutions. This work aims to employ the Newton-Raphson approach to ascertain the convergence (approximate solution in variables) of the equations of a nonlinear infectious disease model after multiple iterations using Matlab. After that, an Excel program is used to plot the iteration graph.