So if I get:
h AUC(after 2 hours)
0.01 335.40257585727842
0.005 335.87803342989893
Can I presume that 335 is accurate result? (without knowing the part after comma).
If h=0.01 does O(h5) mean that up to the 0.015 I get accurate digits?
And should I count O(h5) or...
Ok, I understand that if one set of results differs much from another set (with different step) then the step should be decreased until differences won' tbe large.
One more question :)
Here we are using fixed-step. Is it difficult to implement variable step size?
Thank you in advance!
Thank you!
And regarding errors - I should run the programm with step = H/2 and compare results, however on what basis? - I don't know the exact result that should be. Should I do it one more time and check if the results vary much?
Thank you :)
Everything is working perfectly! But if you had a moment could you explain to me the idea? We use RK to integrate x, and isn't RK designated for differential equations?
Thank you for your answer! :)
In each step, which is equal to time interval (0.01) I calculate the value of x, so as a result I have a List<Double> of 500 x values (5 hours). But how to use them to get AUC? :)
I am full of admiration that you find a time to support us on the forum :)
x - glucose level
y - insuline level
Y - AUC of the glucose level function
I need AUC to calculate http://en.wikipedia.org/wiki/Glycemic_index"
So, as I need AUC under x (as in previous image), on vertical axis...
Thank you. I understand everything (are you a teacher? :) but one thing:
How do we know that? Why with respect to x, not to t?
And as far as error is concerned - I start with half smaller step size, and then substract results?
Thank you again!
Thank you for your answers!
Could you explain in more details where dY/dt = y fdx(x, y, t) came from?
And to calculate error do I understand it correctly that I have to run the same programme with H=0.01/2 and compare results?
Thank you one more time!
Yes.
Sample graph is like the one in the attachment. So, as you see x increases, however after some time it dramatically increases, because what I am (We are) creating is glucose-insuline model, and when glucose level increases more insuline is produced and it makes glucose level decrease...
My results are for calculations - I need to know the exact value od AUC (not for printing, just for forward calculations).
Do you mean that if I use the same (4th order) RK solver I will get AUC? Could you provide more details?
Thank you very much!
Hi :)
Thank you again!
And one more question...
I would like to calculate Area Under the Curve that I printed after having resolved the equations. I know I can do this with rectangle method, adding the areas of each rectangle, however I have a premonition that it has huge error then. What do...