Comparative Study of Numerical Methods for Solving Non-linear Equations Using Manual Computation

Isaac Azure,Louis Doabil,Golbert Aloliga

doi:10.11648/j.ml.20190504.11

Abstract

This paper aims at comparing the performance in relation to the rate of convergence of five numerical methods namely, the Bisection method, Newton Raphson method, Regula Falsi method, Secant method, and Fixed Point Iteration method. A manual computational algorithm is developed for each of the methods and each one of them is employed to solve a root - finding problem manually with the help of an TI - inspire instrument. The outcome of the computations showed that all methods converged to an exact root of 1.56155, however the Bisection method converged at the 14th iteration, Fixed Point Iterative Method converged at 7th iteration, Secant method converged at the 5th iteration and Regula Falsi and Newton Raphson methods converged at the 2nd iteration, suggesting that Newton Raphson and Regula Falsi methods are more efficient in computing the roots of a nonlinear quadratic equation.

Highlights

When real life problems are modelled into mathematical equations in an attempt to solve a problem, the equations are often linear or nonlinear in nature
One critical challenge Newton Raphson method is faced with, which serves as a de-motivation for its usage is the fact that the derivative of the function given must always be found before proceeding to find the root of the function
Fixed Point Iteration method to solve the nonlinear equation (19). It converged to an exact root of 1.56155 after the 8th

Summary

Introduction

When real life problems are modelled into mathematical equations in an attempt to solve a problem, the equations are often linear or nonlinear in nature. Root Finding Problems arise in several fields of studies including Engineering, Chemistry, Agriculture, Biosciences and so on This is as a result of the fact that unknown variables will always appear in problem formula involving real life problems. Its main novelty is that it can be used to compute both zeros and extrema through a single interpolation formula generalized [7] This method is based on the assumption that the graph of y = f(n) in the small interval [an, bn] can be represented by the chord joining (an, f(an)) and (bn, f(bn)). Write the equation in the form f(x) = 0 Step 2: Test for values of x using the function f(x) to obtain the interval (xn, xn−1) in which the real root lies.

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Conclusion