Timeline for A system of ordinary differential equations is being recognized as a DAE
Current License: CC BY-SA 4.0
17 events
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| Sep 3, 2021 at 9:42 | comment | added | edgardeitor | Oh you are right. My bad. The problem is that the first six equations of the system form a linear system or equations in the derivatives of the variables but the last equation is not so simple to solve for the free variable. In fact it will have two solutions related to the direction of the curve (forward or backward). I am not sure about the cost of that for Mathematica, but I will try. | |
| Sep 3, 2021 at 4:06 | comment | added | Michael E2 | The error message is not talking about the initial conditions for the derivatives. I wasn't either. It's the ODE that has to be solved for the (highest order) derivatives in order to use a non-IDA method. | |
| Sep 2, 2021 at 23:44 | comment | added | edgardeitor | I have tried giving the initial conditions for the derivatives but the warnings are still the same... | |
| Sep 2, 2021 at 18:00 | history | tweeted | twitter.com/StackMma/status/1433489951723753479 | ||
| Sep 2, 2021 at 15:23 | comment | added | Michael E2 |
The error message says basically that Solve failed to solve for the derivatives. If NDSolve cannot get the system into the explicit form $x’(t) = f(t, x(t))$, then it has to use an implicit integrator, and I think IDA is the only method available. If you can solve for the derivatives and put the ODE in the form $x’(t)=f(t,x(t))$, then it should make non-IDA methods available.
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| Sep 2, 2021 at 15:11 | comment | added | Alex Trounev | Please, see my answer. | |
| Sep 2, 2021 at 15:10 | answer | added | Alex Trounev | timeline score: 2 | |
| Sep 2, 2021 at 14:30 | comment | added | edgardeitor |
I actually don't know the bifurcation curve so I was considering -0.0001<=ρh<=0.0001 and 0.03<=ν<=0.05 for no actual reason. That could change after I see the curve, of course
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| Sep 2, 2021 at 14:25 | comment | added | Alex Trounev |
Ok! It is nice approach (+1) in general case, but not in this particular case. In what region do you try to plot auxiliarfunction==0?
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| Sep 2, 2021 at 11:39 | comment | added | edgardeitor |
The functions f1aux, f2aux, f3aux and f4aux are used to take into account the equations for the equilibrium point, while det and der are the expressions used to find and continue the Turing bifurcation curve
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| Sep 2, 2021 at 11:37 | comment | added | edgardeitor |
Those conditions can be set with the equations det==0 and der==0. In this case, jacobianmat - μ*diffmatrix is the jacobian matrix of the system including diffusion. As you can see, the function auxiliarfunction takes into account everything I have said. It has the equilibrium point evaluated, and a solution to the equation der==0, that has to do with the derivative of the zero-eigenvalue. The problem is that that function is a mess and I haven't been able to get an implicit plot out of it. Instead, I am trying to parametrize the curve.
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| Sep 2, 2021 at 11:26 | comment | added | edgardeitor |
I've got a system of four reaction-diffusion equations. f1, f2, f3 and f4 are only the kinetics. I want to plot a Turing bifurcation curve. I know that the third equilibrium of the system goes through this bifurcation when we take the parameter values provided. The conditions for this bifurcation are essentially two: 1.-The determinant of the jacobian matrix of the system including diffusion is equal to zero and 2.-The derivative of the zero-eigenvalue of the system including diffusion is equal to zero.
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| Sep 2, 2021 at 1:51 | comment | added | Alex Trounev | Could you explain mathematically what do you try to solve? | |
| Sep 1, 2021 at 15:04 | history | edited | edgardeitor | CC BY-SA 4.0 |
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| Sep 1, 2021 at 14:45 | history | edited | edgardeitor | CC BY-SA 4.0 |
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| Sep 1, 2021 at 14:07 | history | edited | edgardeitor | CC BY-SA 4.0 |
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| Sep 1, 2021 at 14:00 | history | asked | edgardeitor | CC BY-SA 4.0 |