Evaluating Three Methods of Solving Equations.

The first 200 words of this essay...

Maths C3 Coursework

Introduction

I'm going to look at 3 methods used to find the roots of an equation. First the decimal search or the sign change method; second, the Newton-Raphson method and third the fixed point iteration method, also called the x=g(x) method. I will then critically compare the three methods to find their advantages and disadvantages and will finally talk about how the current technology improves the efficiency of these methods.

Change of sign method: Decimal search

This is the first method. In this method we first determine two nearest values of x within which the function changes sign from +ve to -ve or vice versa. This is done with the help of the function graph. Roots of the equation will obviously lie within these two values of x. We then calculate f(x) within this range by splitting the values of x as necessary. Again we note down two adjacent values of x, within this smaller range, between which the function changes sign again and repeat the same exercise again and again till we reach as close to the root as we wish to.

Let me illustrate the point by solving an equation