Timeline for Differential complex equations in cosmological problem
Current License: CC BY-SA 4.0
8 events
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| Jan 25 at 4:11 | comment | added | Julian Yussef |
I do not expect the solution to be described by WeierstrassP. On the contrary, I was expecting to be a sinusoidal function to describe the solution.
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| Jan 25 at 2:05 | comment | added | Julian Yussef |
Yeah, I got your exact solution, however when I put the initial conditions, it seems that the solution goes crazy with the WeierstrassP function, which is something unusual since I would expect the same sinusoidal behavior as the one you described and posted. DSolveValue[u''[t] + %[[2]] u[t] == 0, u[t], t] /. {C[1] -> 0.000259728 E^(I (-0.0249668)), C[2] -> 1925.09 E^(I (-1.59576))}
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| Jan 25 at 2:01 | comment | added | bbgodfrey |
@JulianYussef The shape of the curve will be sinusoidal, with the amplitude slowly growing until f = 0 is reached, then it will drop exponentially toward zero as shown in my last plot. (Conceivably, it also could grow exponentially from there, but that does not sound physically realistic.) Qualitatively, the solution depends on the shape of f and will differ significantly from my prediction only if f increases with t instead of passing through zero.
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| Jan 25 at 1:53 | comment | added | Julian Yussef |
I am trying to match the behavior of this solution with another one that I already know. It has to be similar to the last plot in my post, but using the initial conditions I proposed, I got -(-1)^(2/3) 6^(1/3)WeierstrassP[(-(1/6))^(1/3) ((0.000259647 - 6.4839*10^-6 I) + t), {0, -48.0523 - 1924.49 I}] as a solution, but its plot is not what I expected, since the perturbations should follow a Sine, Cosine behavior that is decreasing as t grows.
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| Jan 25 at 1:42 | comment | added | bbgodfrey |
You could use the ode4 boundary conditions to initialized the WKB approximation, then match that solution to the Airy solution near f = 0. However, with of order a million oscillations over that range, the oscillation phase probably would be quite uncertain by time f = 0 is reached. What are you actually trying to determine, the form of the solution or its precise value at some point in t?
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| Jan 25 at 1:20 | comment | added | Julian Yussef |
Nice solution to this. However, I do not understand where can I use the proposed initial conditions for the ode4. Do I have to write them in the C[1] and C[2]?
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| Jan 24 at 23:59 | history | edited | bbgodfrey | CC BY-SA 4.0 |
improved wording
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| Jan 24 at 23:51 | history | answered | bbgodfrey | CC BY-SA 4.0 |