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These are answers submitted by archstevej

Thanks, that was driving me crazy. There should be an easier way to turn it off.
Hi Scott, I tried that, but did not see the call. What is the code for that call, maybe my eyes are missing it. Thanks, Steve
Thanks for this discussion.

If I plug Eq1 into Eq2, I will still have two differential equations (ignoring H(t))---Rdot and Wdot.

When I solve this system using numerical starting values, I get soultions for R and W.

However, I could have solved the system without plugging Eq1 into Eq2. In this case, I get the same R and W solutions.

But, if Rdot=0, I get different answers when plugging Eq1 into Eq2 than I do when I solve the system in a less reduced form. So, I am still not sure which way is more correct.


Thats great, thanks. I am not sure where to find code for stuff like that, other than to look here!



That was just a typo from me copying into here. I get the error when the parantheses are correct. I don't think the int command knows to take the results from sol1 to use for W(t), R(t), and H(t).

Any other suggestions would be helpful. Thanks.






Instead of thinking it as time going backwards, can I think about it as though the direction of the subject at hand either going up or down? For example, if I have a boulder teetering on a ledge halfway up a mountain. My differential equation might explain the movement of the boulder further up the mountain with time. But, if I put a negative in front of the differential equation I am actually explaining pushing the boulder back down the mountain to reach a steady  equilibrium state.

What I have been assuming is that my model (without any negative signs) would explain the problem so that it is simulated "forward" in the path of least resistance. In this case, that would be decreasing pumping in time as costs became higher. But, this is not necessarily the case. So, I need the negative sign to bring the simulation to the steady state point.

Does this make any sense?




Right, I got similar values for the equilibrium. I constantly adjust the parameters, so mine is a little different now. I see what you mean about seeing how things were in the past. But, I am trying to predict what will happen given today's level of pumping water. So, I would expect to be analyzing some future condition. I do think this discussion is helping. Thanks.

What if there is no equilibrium when you run the model forward. In my simulation, the ODEs seem to leave an equilibrium due to the initial conditions I choose. If I run it backwards, it looks as though the equilibrium is reached in the future.



Okay, thanks for your help on this. I am seeing what I need to learn more about. Do you know what literature I could read to better understand this?

I am not so sure I buy running time backwards for my situation, even if it is for all of my differential equations. I have a social discount factor in the model, and it seems counter intuitive to do it backwards. Would the predator-prey model be something that can go backwards, for example?

Thanks for your help on this!



The topic is a hydrology and water pumping project. If time is run backwards, does this mean that starting points are actually ending points? The advisor is not the best communicator!

What you say makes sense. I wonder though, does the -1 change the nature of the problem to the point where it does not actually represent reality? I am trying simulate a real life situation.  With the negatives, my  result looks better. But, not sure I can stand by it. Is there any way to check to see if what I am doing is okay?

Dang, this is complicated!





I am sorry for taking so long to get back to this. But, I still have a problem. I am working on a system of ODEs that blows up when I do a numerical solution. One of my advisors says to multiply the ODEs by -1 to reverse the role of the eigen values. I only vaguely understand this. Would you be able to point me in the right direction to figure this out? When I do this, my results are much more stable.




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