Simpson's & Trapezoidal Rule (1 Viewer)

[the_matrix]

Hello!

Could someone clarify to me what one sub-interval, interval, strips, etc (every other term you know) means in terms of number of function values for Simpson's and Trapezoidal rule?

I know what application means for both rules so you don't have to waste time explaining that one as it can be a hassle.

My teacher isn't very good and he doesn't go through these terms so when we encounter them, we're like wth..
It'd be seriously helpful if you could help me with every term you know as my HSC mid year exams are on in 2 weeks.

Thanks!

 

[ml125]

Re: Simpson's & Trapezoidal Rule

Subintervals are sometimes referred to as intervals. Each function value you use will lie on either side of each subinterval, therefore there will always be one more function value than you have subintervals. Eg. if o represents subintervals and | represents function values it would be like this: |o|o|o| If you look at the repeater patterns for each; Trapezoidal (1 2 2 2 1) and Simpson's (1 4 2 4 1), you can see that for Trapezoidal Rule there are no limitations as there is a uniform pattern. For Simpson's Rule however, there must an odd number of function values ie. an even number of subintervals.

One way I differentiate the two rules is that Trapezoidal only uses 1 and 2 + Simpson's uses 1, 2, 3 and 4 hahaha

My explanation kinda seems like a mess but I hope you can get at least something out of that lol good luck

 

[the_matrix]

oh yes yes i can see where you're going! thanks

 

[Ambility]

Trapezoidal rule is pretty straight forward: an application has one subinterval and for n applications there are n+1 function values.

The Simpson's rule is a little more complex: one application has two subintervals. This means there is a beginning, middle and end function value for each application. Remember that intervals next to each other share function values. One application has three function values, two applications has five function values (one is shared), three applications has seven function values (two are shared).