Numerical Solutions of Equations.

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P2 Maths Coursework

Numerical Solutions of Equations

HANNAN SHAH

Introduction

In this coursework I intend to use numerical methods to find the solutions of equations that cannot be solved algebraically. Many simple equations can be solved using methods such as factorising or the quadratic formula but such methods cannot be applied to more complicated equations. My intention is to use three methods of numerical analysis to solve some of these more complex equations, show problems associated with these methods and then to compare their relative merits. The methods I will be using are decimal search, fixed point iteration using Newton-Raphson and fixed point iteration after rearranging f(x) = 0 into the form x = g(x).

Decimal Search

Assuming that you are looking for the roots of the equation f(x) = 0 you want to find the values of x for which the graph of y = f(x) crosses the x-axis. As y = f(x) crosses the x-axis, f(x) changes sign (from + to -), provided that f(x) is continuous.

Using decimal search I will attempt to find one root of the equation y = x5+4x²-1. The graph for this function is shown below.