Implementing Richardson Extrapolation

The_Provost · July 21, 2017, 13:11

Hello,

I have a set of data for radius as a function of time. Please note that I do not have the expression of the function, I only have the values of radius at a given time. I want to implement Richardson extrapolation to these values using MATLAB. I am not sure, how to go about writing the code. Because most of the examples are using an expression as in "y=f(x)". Any help would be appreciated.

Thanks.

LuckyTran · July 21, 2017, 17:05

https://en.wikipedia.org/wiki/Richardson_extrapolation

Implement the second line R(h,k)

The_Provost · July 21, 2017, 17:15

Quote:

Originally Posted by LuckyTran

https://en.wikipedia.org/wiki/Richardson_extrapolation

Implement the second line R(h,k)

Thanks, however, what is "k", and "n" here? Also in my case, I have radius as a function of time, so will "h" be the time for my code?

Thanks for your help.

LuckyTran · July 21, 2017, 17:34

h is the step-size

For example, if you want to R(t1), R(t2), R(t3) and want to extrapolate to R(t4) then h is delta in t (t2-t1, t3-t2, etc). k is the ratio deltas which is often 2 for uniformly sampled data. n is the order of convergence which you should already know. If not, you have to estimate n using another technique.

The_Provost · July 22, 2017, 11:23

Thanks a lot for the explanation.

Sent from my iPhone using CFD Online Forum mobile app

July 21, 2017, 13:11	Implementing Richardson Extrapolation	#1
The_Provost New Member The_Provost Join Date: Sep 2014 Location: USA Posts: 15 Rep Power: 11	Hello, I have a set of data for radius as a function of time. Please note that I do not have the expression of the function, I only have the values of radius at a given time. I want to implement Richardson extrapolation to these values using MATLAB. I am not sure, how to go about writing the code. Because most of the examples are using an expression as in "y=f(x)". Any help would be appreciated. Thanks.

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July 21, 2017, 17:05		#2
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,673 Rep Power: 65	https://en.wikipedia.org/wiki/Richardson_extrapolation Implement the second line R(h,k)

July 21, 2017, 17:34		#4
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,673 Rep Power: 65	h is the step-size For example, if you want to R(t1), R(t2), R(t3) and want to extrapolate to R(t4) then h is delta in t (t2-t1, t3-t2, etc). k is the ratio deltas which is often 2 for uniformly sampled data. n is the order of convergence which you should already know. If not, you have to estimate n using another technique.

July 22, 2017, 11:23		#5
The_Provost New Member The_Provost Join Date: Sep 2014 Location: USA Posts: 15 Rep Power: 11	Thanks a lot for the explanation. Sent from my iPhone using CFD Online Forum mobile app