Hi Brombo,
Thank you for the update. It seems my previous posts didn't show up.
Anyway, you result doesn't match the result in Maple and the numerical
evalution of the integral in Python:
Would be wonderful if we'd find an analytical solution.
Op vrijdag 10 februari 2023 om 01:08:56 UTC+1 schreef brombo:
> Attached are latest results (I had calculated the roots of the quadratic
> wrong) and a plot -
> On 2/8/23 4:24 AM, 'Tom van Woudenberg' via sympy wrote:
>
> Hi Brombo,
>
> Thank you for the extensive working-out. I really appreciate that!
> However, the result doesn't seem to match the result in got in Maple
> (below result in Python for N(t):
>
> [image: Schermafbeelding 2023-02-08 094041.jpg]
> Do you have any ideas on the difference?
> Op woensdag 8 februari 2023 om 01:10:05 UTC+1 schreef brombo:
>
>> I didn't proof read well enough. Typo in equation 4. Correction attached
>> On 2/7/23 3:02 AM, 'Tom van Woudenberg' via sympy wrote:
>>
>> Thank you brombo, I'll take a closer look at the file you send me!
>>
>> Op maandag 6 februari 2023 om 22:29:25 UTC+1 schreef brombo:
>>
>>> I cleaned things up here is what the notebook looks like (see attached
>>> html) -
>>>
>>>
>>> On 2/6/23 10:36 AM, 'Tom van Woudenberg' via sympy wrote:
>>>
>>> Hi there,
>>>
>>> When trying to solve a integral as part of a manual inverse fourier
>>> transform, SymPy return the unevaluated integral. Does anybody know if
>>> SymPy is able to solve this integral with some help? It would be good
>>> enough if I'd be able to obtain the result for specific values of t.
>>>
>>> import sympy as sp
>>> phi,t = sp.symbols('phi,t',real=True)
>>> sp.I*(1 -
>>> sp.exp(4*sp.I*sp.pi*phi))*sp.exp(-8*sp.I*sp.pi*phi)/(2*sp.pi*phi*(-4*sp.pi**2*phi**2
>>>
>>> + 1.5*sp.I*sp.pi*phi + 4))
>>> solution_numeric = 1 / sp.pi * sp.integrate(sp.re
>>> (solution_in_frequency_domain_numeric*sp.exp(sp.I*2*phi*t)),(phi,0,4))
>>> print(solution_numeric)
>>>
>>> returns:
>>> (Integral(sin(4*pi*phi)*re(exp(2*I*phi*t)/(-4*pi**2*phi**2*exp(8*I*pi*phi)
>>> + 1.5*I*pi*phi*exp(8*I*pi*phi) + 4*exp(8*I*pi*phi))), (phi, 0, 4)) +
>>> Integral(cos(4*pi*phi)*im(exp(2*I*phi*t)/(-4*pi**2*phi**2*exp(8*I*pi*phi) +
>>> 1.5*I*pi*phi*exp(8*I*pi*phi) + 4*exp(8*I*pi*phi))), (phi, 0, 4)) +
>>> Integral(-im(exp(2*I*phi*t)/(-4*pi**2*phi**2*exp(8*I*pi*phi) +
>>> 1.5*I*pi*phi*exp(8*I*pi*phi) + 4*exp(8*I*pi*phi))), (phi, 0,
>>> 4)))/(2*pi**2*phi)
>>>
>>> Plotting the result for t,0,15 should give this result according to
>>> Maple:
>>> [image: Schermafbeelding 2023-02-06 163521.jpg]
>>>
>>> Kind regards,
>>> Tom van Woudenberg
>>> Delft University of Technology
>>>
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