Passing NDSolve through NIntegrate?

Questions
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1

Hello everyone,

I was wondering: is it possible to solve a differential equation over a certain domain using NDSolve and pass that solution through NIntegrate? Any suggestions would be greatly appreciated!

Alex

testt.nb 16-06-35-484.nb (210 KB)

2

Some problems with the code

h is a list, not a function. Need

h = h /. slv // First

And in the definition of B, h needs to be h[t].

What is g? It is used in the definition of B but is not defined. Easy to spot since it is colored blue.

3

Sorry about that! I updated the notebook.

4

OK, I evaluated the updated notebook and there are no errors and there is no NIntegrate. So, I am confused. What are you trying to integrate?

5

I updated it again; I am so sorry for the confusion! I am trying to solve h’[t] numerically using NDSolve, plug the resulting h[t] values into b*(1-cg)h[t]/K + b(1-cg)g(1 - h[t]/K) - d*h[t]/K and numerically integrate the resulting curve. Is this possible?

Alex

6

Hi Alex,

Thanks for changing the filename this time. The code in testt.nb 16-06-35-484.nb works fine for me. Make sure you start from a clean kernel. The problem is with the plotting because NIntegrate will be called hundreds of times. You can speed up the integration like this

B[u_?NumericQ] := 
 NIntegrate[(1 - c*g)*h[t]/K + g*(1 - c*g)*(1 - h[t]/K) - (h[t])/K, {t, A, u}, 
  Method -> {Automatic, "SymbolicProcessing" -> 0}]

Then this is pretty fast

Plot[Exp[B[u]], {u, 0, 250}]

10339plot.png
10339plot.png360×226 8.66 KB

Looks like the integral starts diverging around x = 225. Please verify that the change to B to speed it up is not impacting accuracy.

7

WOW I really did not think this would be possible. Thank you SO MUCH!!

8

Hello again,

I was told I should not ask this question via a new discussion, so I was wondering: do you know how I could avoid receiving an error in the attached code and how I might make the code run faster? I am trying to pass one NIntegrate solution through another and subsequently pass that resulting function through NIntegrate. The code is not only slow but also gives me an answer that I think is wrong.

Alex

test 1.nb (12.4 KB)