Thread: Numerical Analysis - Composite rule

I am trying to find the more general composite rule of this basic rule :

Integral from 0 to 1 of a function of x = h/12[5f(0) + 8f(1) - f(2)]

This works with h = 1 on f(x) = x for example, but I cannot figure out how to get it to work if you take h = 1/2 for example. Please help! I figured this out but it doesn't seem to work.

h/12[f0+8f1+4f2+8f3+....+4fn-2+8fn-1 -fn]

Thanks

Originally Posted by purakanui

I am trying to find the more general composite rule of this basic rule :

Integral from 0 to 1 of a function of x = h/12[5f(0) + 8f(1) - f(2)]

Your basic quadrature rule should not depend on , you probably mean:



It would also help if you posted the complete question as worded in the original

This works with h = 1 on f(x) = x for example, but I cannot figure out how to get it to work if you take h = 1/2 for example. Please help! I figured this out but it doesn't seem to work.

h/12[f0+8f1+4f2+8f3+....+4fn-2+8fn-1 -fn]

Thanks

You build the composite rule from:



for and

CB

Let Q(f) be the quadrature rule for Integral from 0 to h f(x)dx that involves f(0), f(h) and f(2h). Ive found Q to be the above h/12[5f0 + 8f(h) - f(2h)]. The question I am stuck on is...

Find the corresponding composite rule for integral from 0 to 1 f(x)dx.

So it says h = 1. Giving: 1/12[5f0 + 8f1 - f2]. But i do not know how to expand this using the composite rule. I thought it would give:

1/12[(5f0 + 8f1 - f2) + (5f2 + 8f3 - f4) +...+(5fn-2 + 8fn-1 - fn)]

= 1/12[5f0 + 8f1 + 4f2 + 8f3 +...+4fn-2 + 8fn-1 - fn]

But that doesn't seem to work, please help now??? Cheers

Originally Posted by purakanui

Let Q(f) be the quadrature rule for Integral from 0 to h f(x)dx that involves f(0), f(h) and f(2h). Ive found Q to be the above h/12[5f0 + 8f(h) - f(2h)]. The question I am stuck on is...

Find the corresponding composite rule for integral from 0 to 1 f(x)dx.

So it says h = 1. Giving: 1/12[5f0 + 8f1 - f2]. But i do not know how to expand this using the composite rule. I thought it would give:

1/12[(5f0 + 8f1 - f2) + (5f2 + 8f3 - f4) +...+(5fn-2 + 8fn-1 - fn)]

= 1/12[5f0 + 8f1 + 4f2 + 8f3 +...+4fn-2 + 8fn-1 - fn]

But that doesn't seem to work, please help now??? Cheers

Your composite rule should start:


..................................

.............. .

Where

CB