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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…

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OCRMEI Numerical Methods
Methods You Need to Know




1 + sin ANS and then press = . This will give a value for x1.

The Solution of Equations

x1 1

x2 1.357008101

x3 1.406141602

x4 1.409423644

x5 1.409612592

x6 1.409623354


4) The NewtonRaphson Method

The NewtonRaphson Method is an iterative…

Page 3

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OCRMEI Numerical Methods
Methods You Need to Know




Numerical Integration

1) The Midpoint Rule

The Midpoint Rule is a way of estimating the area under a curve (integration) and is found by
splitting the area underneath the curve into equals strips of width h . Here is the general
equation…

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OCRMEI Numerical Methods
Methods You Need to Know



Numerical Integration

There are also some other formulae that you should learn for the exam:


T 2n = T n+
2
Mn


4T 2n-T n
Sn = 3

4M 2n-M n
"Best Midpoint" = 3

4T 2n-T n
"Best Trapezium" = 3…

Page 5

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OCRMEI Numerical Methods
Methods You Need to Know



Numerical Differentiation

1) The Forward Difference Method

This method of numerical differentiation finds the gradient of the tangent to the curve between
the points x and x + h . This is not the most reliable method but is very simple and…

Page 6

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OCRMEI Numerical Methods
Methods You Need to Know



Approximating Functions

Finite Difference Tables:

This is where you find the difference between all of your f (x) values as this determines what
order you function is of. Here is an example:

x x0 x1 x2 x3


f (x) f0 f1 f2…

Page 7

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OCRMEI Numerical Methods
Methods You Need to Know



NOTE: This formula is given in the exam under the name: "Newton's Forward Difference
Formula".

Approximating Functions

2) Lagrange's Method

Lagrange provided a method to approximate a function outside of the data set:

For a linear graph that passes through (a, A)…

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