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Simple example to solve ODE
Posted May 10, 2013, 1:17 p.m. EDT Modeling Tools & Definitions, Parameters, Variables, & Functions, Studies & Solvers Version 4.3a 2 Replies
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I am a complete newbie with COMSOL (I have the MultiPhysics module, version 4.3a), and I have only followed some initial tutorial examples in the manual (e.g. "the wrench").
However, as I understood, there are also ways to solve ODEs (ordinary differential equations). I wanted to start with something really simple, and on the internet I found some example involving the predatory model:
#rabbits: dr/dt = a*r - b*r*f
#foxes: df/dt = -c*f + d*r*f
However, the example I found is clearly meant for a different COMSOL version because the description of buttons/menus to use does not correspond to my version.
To give it a go anyway, I used the "Global ODEs and DAEs" node, and in the "Global Equations 1" settings window, defined:
r*(a-b*f)-rt (initial value r: 100, initial value rt: 0)
-f*(c-d*r)-ft (initial value f: 100, initial value ft: 0)
My question is (and this might come from a complete misunderstanding of how COMSOL works):
- Where do I define the upper and lower bounds for t? (In the geometry, but how?)
- how do I get a plot showing r and f versus t? (Do I need to use "parameter sweep" for this?)
- Is it possible to just solve a 1-D ODE without selecting any kind of other physics models?
- Is there any example around for version 4.3a?
- (I actually tried to just click on "Study1->Calculate" and while the program does not complain, I also have no idea how to get the plot I want)
Best regards,
Machiel
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Regarding your questions:
1. Where do I define the upper and lower bounds for t? (In the geometry, but how?)
You add a Time Dependent study to the model (directly in the Model Wizard or by right-clicking the root node in the model tree). Then you define the times in the settings window for the Step 1: Time Dependent node; the default setting is "range(0,0.1,1), which means that time runs from 0 to 1 s with steps of 0.1 s.
2. How do I get a plot showing r and f versus t? (Do I need to use "parameter sweep" for this?)
No, a 1D Plot Group with a Global plot node should appear automatically. In the settings window for the Global node, you can add r and f as the state variables mod1.r and mod1.f (in the table of expressions under "y-Axis Data") to plot both of them as a plot of r and f versus t.
3. Is it possible to just solve a 1-D ODE without selecting any kind of other physics models?
Yes, you can add just an Global ODEs and DAEs user interface (and then select 0D as the model's geometry dimension if you have no geometry).
4. Is there any example around for version 4.3a?
This predator-prey model is described in the COMSOL documentation as the Lotka-Volterra equations. The documentation shows how to enter the equations in the settings window for Global Equations.
5. (I actually tried to just click on "Study1->Calculate" and while the program does not complain, I also have no idea how to get the plot I want)
This is probably because there is no Time Dependent study in your model, but I'm not sure.
Hope this helps.
Best regards,
Magnus Ringh, COMSOL
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Thank you very much. You were right, what was missing was the Time Dependent study.
Best regards,
Machiel