Linked Questions
24 questions linked to/from Workarounds for a possible bug in the linearity of FourierTransform
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Can I take the Fourier transform of a PDE in both sides? [duplicate]
I want to know if it is possible to use a PDE in the function FourierTransform instead of a function.
Consider for example the simple case for the heat equation
...
user86304
0
votes
0
answers
98
views
FourierTransform a differental-equations [duplicate]
I want to use the command FourierTransform to transform a differential equations from time - domain to complex frequency domain but it don't works. My code is ...
user39156
2
votes
0
answers
74
views
How do I let Fourier Transform know that it is a linear operator? [duplicate]
I have the following issue with FourierTransform, Fourier transform doesn't seem to know it is a linear operator.
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1
vote
0
answers
49
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Fourier transform of an equation [duplicate]
I have the following equation:
$$m \frac{d^2 x}{dt^2} = -Kx - \alpha \frac{dx}{dt} + f(t) $$
Which I introduced into Mathematica as:
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- 153
20
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3
answers
2k
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Numerically solve the initial value problem for the 1-D wave equation
I want to solve the standard 1-dimensional wave equation $y_{xx}=y_{tt}$ using NDSolve (for $y(x,t)$) with the following conditions:
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- 313
6
votes
2
answers
2k
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Bilateral Laplace Transform
I am trying to solve a linear ODE for a Kolmogorov forward equation to get a stationary distribution of a random variable. The easiest approach may be to transform the ODE with a two-sided Laplace ...
- 967
4
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2
answers
3k
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Obtaining the Fourier transform of an operator
We know that if we have a function $f(x)$, and we call $g(\omega)$ its Fourier transform, then the Fourier transform of $x f(x)$ is
$$\imath \frac{\mathrm{d} g(\omega))}{\mathrm{d}\omega} $$
and ...
- 41
6
votes
2
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406
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Prove linearity of integration [duplicate]
I'd like to prove the linearity of integration over one real variable ($x$).
Integrate[f[x] + b g[x], x] == Integrate[f[x],x] + b Integrate[g[x],x]
which I was ...
- 41.2k
7
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1
answer
428
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Problems with DSolve and NDSolve for Dirichlet problem on an annulus
To solve the Dirichlet problem on an annulus, I do the following in 12.2 on Windows 10 Pro
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- 26.4k
2
votes
1
answer
1k
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Solving the heat equation on the semi-infinite rod
Cross posted in scicomp.SE.
I want to test the solution which is given below is right by Mathematica.
Please look the post in mathstackexhange
or
Please look below.
Question: Solve the ...
- 543
5
votes
2
answers
1k
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Solve PDE with DiracDelta function
This question is related to Analytic solution of dynamic Euler–Bernoulli beam equation with compatibility condition. I think it is more appropriate to open another question on this topic.
In the ...
- 2,571
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1
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403
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Possible bug with FourierTransform linearity
Each component is easily transformed but the sum is not:
FourierTransform[f''[x], x, k]
FourierTransform[f'[x], x, k]
...
Kuba♦
- 137k
9
votes
1
answer
182
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LaplaceTransform works well with x[t], but doesn't recognize x[1][t], how to make it works for x[1][t]?
Bug introduced in 12.2(?), persisting through 14.0 or later.
When I am solving odes using LaplaceTransform, I found that LaplaceTransform works well with u[t] or y[...
- 1,323
7
votes
1
answer
272
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Derivative of real antisymmetric matrix in mathematica
Is it possible to find the derivative of components of a real antisymmetric matrix using index notation? Eg: I have a very large real antisymmetric matrix. Then from Matrix Cookbook, we know the ...
- 1,225
3
votes
2
answers
221
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How to make an organised investigation of branch cuts from a solution to a differential equation
I am attempting to solve two differential equations. The solution gives equations that have branch cuts. I need to choose appropriate branch cuts for my boundary conditions. How do I find the correct ...
- 16.5k
3
votes
1
answer
288
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How to implement the finiteness condition for a PDE?
I have a PDE
$$u_t=u_{yy}+u_{zz}$$
subject to the following initial and boundary conditions
$$u(y=0,z>0,t>0)=1,$$
$$u(y=0,z<0,t>0)=0,$$
$$u(y=10,z,t>0)=0,$$
$$u(y,z=\pm10,t)\,\, \...
- 11.9k
3
votes
2
answers
155
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GreenFunction Computation for perturbed Laplacian
I am happy computing the Green function for the Laplacian
Gsol := GreenFunction[{-Laplacian[u[x, y], {x, y}]},
u[x, y], {x, y} ∈ FullRegion[2], {m, n}]
it gives ...
- 205
2
votes
1
answer
171
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unknown cause of scaling factors in NDSolve solutions to a partial differential equation
I am trying to solve a coupled diffusion partial differential equation with a Gaussian profile at t = 0. I would like to see how the two functions, y and z, evolve in time and in one dimension. This ...
- 2,815
3
votes
1
answer
87
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Nice output for FourierTransform
I want to demonstrate FourierTransform in a lecture. However if you give FourierTransform a differential equation it does not ...
- 16.5k
2
votes
1
answer
73
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Difference between FourierTransform and LaplaceTransform [duplicate]
There is an equation for example：
eqn=D[c[x, t], t] == d D[c[x, t], x, x];
When I make a LaplaceTransform of it:
...
1
vote
1
answer
71
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Is there an option for InverseLaplaceTransform to make Mathematica use the convolution theorem when feasible?
By default, it appears that Mathematica won't use the convolution theorem to write an inverse Laplace transform in the form of a convolution of two functions.
For example, ...
- 453
0
votes
0
answers
109
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For Fourier Transform with $ x(t) $, how to obtain result in terms of $ X(f) $?
I have a function $ x(t) $ and I denoted its Fourier transformation as $ X(f) $. I want to get the Fourier transformation of $ x(t)\mathrm e^{2\mathrm i \pi f_0 t} $, and I know the result is $ X(f-...
- 3,469
0
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1
answer
96
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Collect terms in Fourier Transform
I want to collect terms in x from a product of polynomials and Fourier transform. So I try following code:
...
- 15
1
vote
0
answers
66
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Why this Solve cannot be solved [duplicate]
Solve[Sum[p*a[i], {i, 1, n}] == 0, p, Reals]
Solve[p*Sum[a[i], {i, 1, n}] == 0, p, Reals]
The first line of code cannot be solved, but when the variable ...
- 151