# MEI Numerical Methods - Methods you need to know

A brief explanation of all the methods you need to know for OCR-MEI NM exam. No graphical interpretations but shart step by step guidelines to help with numerical methods.

- Created by: DanArthur
- Created on: 14-05-13 18:31

First 305 words of the document:

OCRMEI Numerical Methods

Methods You Need to Know

The Solution of Equations

1) The Bisection Method:

For a root in the interval [a, b] , find the midpoint c = a+b

2 . If c has the same sign as a , then let

a = c . If c has the same sign as b , then let b = c . Keep repeating this process until you have

reached the desired level of accuracy. c is the best estimate for the root.

a b Sign of f (a) Sign of f (b) c Sign of f (c)

2) The Method of False Position:

For a root in the interval [a, b] , find a variable c such that c = af f(b )-cf (a)

(b)-f (a) . Likewise with the

Bisection method, if c has the same sign as a , then let a = c . If c has the same sign as b ,

then let b = c . Keep repeating this process until you have reached the desired level of

accuracy. c is the best estimate for the root.

a b Sign of f (a) Sign of f (b) c Sign of f (c)

3) Fixed Point Iteration

Rearrange f (x) so that x = g(x) where g(x) is another function that contains x . From this, you

can create an iterative formula to put into your calculator.

For example:

f (x) = x2 - sin x - 1 has a root in the interval [1, 2] . Use a fixed point iteration to find a root to 4

decimal places:

f (x) = x2 - sin x - 1

x = 1 + sin x

The iterative formula is:

where x0 = 1+2

xr+1 = 1 + sin xr 3

2 = 2 (from interval)

Therefore, you can type 3

2 on your calculator and press = . Then type:

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