This is the result in Python (same as in Maple): [image: downloaden (5).png]
Op vrijdag 10 februari 2023 om 17:31:50 UTC+1 schreef Tom van Woudenberg:
> 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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