18
votes
Accepted
Mathematica and MATLAB giving different results from inverse Laplace transform
You missed one term in Matlab. den=[1,4,2,3,0]; and not den=[1,4,2,3]; The order is important in Matlab. Since you do not have ...
- 130k
15
votes
Numerical inverse Laplace-Hankel transform
The following is not particularly fast and could be more accurate but does make progress toward the goals set in the Question. To begin, consider the analytical properties of ...
- 60k
14
votes
Implement finite Fourier transforms
This post contains several code blocks, you can copy them easily with the help of importCode.
The following is my implementation for finite Fourier transforms. ...
- 60.8k
14
votes
Accepted
Wrong result of Laplace Transformation
Your integral is wrong. Laplace transform is defined from $0$ to $\infty$ not from $-\infty$ to $\infty$. The 2-sided Laplace transform is defined from $-\infty$ to $\infty$ but that is not the ...
- 130k
13
votes
Package for fast spherical harmonic transform in Mathematica?
I am aware that my answer would not be accepted because OP explicitly
demanded a FFT-like method.
I am aware of the fact that the method is not very fast either.
However, it is so simple that I do ...
- 17.2k
13
votes
Accepted
How to set up a spherically symmetric Fourier transform?
Summary: To perform the 3D Fourier Transform of a spherically symmetric function $f(r)$ in Mathematica, use the command
(4 Pi)/k FourierSinTransform[f[r] r, r, k]
...
- 14k
12
votes
Accepted
Bilateral Laplace Transform
Update 2
In v12.3, BilateralLaplaceTransform and InverseBilateralLaplaceTransform are built-in. Their usages are almost the same ...
- 60.8k
12
votes
Accepted
11
votes
Accepted
How can I invert a Laplace transform numerically?
As of v12.2, InverseLaplaceTransform supports numeric Laplace inversion. In addition, there exist at least 6 Mathematica packages for numeric inverse Laplace ...
- 60.8k
11
votes
Solving partial differential equation involving Hilbert transform
I used the method of solving integro-differential equations proposed by Michael E2 on Solving an integro-differential equation with Mathematica
I added new options to his code to solve this problem. ...
- 39.8k
10
votes
Accepted
Inverse Laplace Transform difficulty
InverseLaplaceTransform[(2 s^2 + s + 13)/((s - 1) ((s + 1)^2 + 4)), s, t]
2*E^t + (3/4)IE^((-1 - 2*I)t)
(-1 + E^(4*I*t))
...
- 144k
10
votes
10
votes
Accepted
Correct way of simplifying the result of an integral
Many times Mathematica gives enormous results to simple problems
If Simplify still does not help reduce the antiderivative to what you like, you could always try ...
- 130k
10
votes
Accepted
9
votes
Inverse Laplace transform
I was asked to explain how I arrived at the statement of my comment, regarding the first step of the complete solution.
Here it is:
The y-integral is of the form
...
9
votes
How to obtain that result of the integral in Mathematica?
It's a Fourier integral. With those, Mathematica can confidently venture into generalized function territory and yield things like DiracDelta (hazardous in general)....
- 13.6k
9
votes
Mathematica and MATLAB giving different results from inverse Laplace transform
With Mathematica you can also do the following
...
- 1,745
9
votes
InverseRadon behaves differently from iradon of MATLAB
As it explained in tutorials functions
Radon
and
InverseRadon
are supposed to be used with images only and not with arbitrary ...
- 39.8k
9
votes
3D Fourier transform of 1/r^2
The Fourier transform will be spherically symmetric, so let's set $\vec{k}$ parallel to the $z$-axis without restriction of generality.
First, generalize the integral to the Fourier transform of $r^{...
- 43.6k
8
votes
Accepted
Solving PDE involving Hilbert transform numerically
As I pointed out in a comment above, this problem can be solved by performing a Fourier Transform in x, solving the resulting ODE, and transforming back. The ...
- 60k
8
votes
Accepted
Analytic expression for a Complex Hilbert Transform in Mathematica
This is due to the sum of two very large numbers (coming from CosIntegral and SinhIntegral) being carried out without sufficient ...
- 7,513
8
votes
Accepted
Calculate the Bromwich Integral (Inverse Laplace Transform)
I think one possible issue is that e.g. a+Infinity*I becomes just DirectedInfinity[I] because the "finite" part gets swallowed. ...
- 57.7k
8
votes
Accepted
8
votes
Accepted
InverseMellinTransform producing two different results for the same input?
expr = Gamma[1 + s]/Gamma[1 - s] Gamma[-s]^2;
imt1 = InverseMellinTransform[expr, s, x, GenerateConditions -> True]
...
- 144k
8
votes
Accepted
Inverting integral transform $f(s)=\int_0^\infty g(x) \exp(-s g(x)) \mathbb{d}x$
In the math.stackexchange post I have shown that
$$\left\{\theta(y-a)-\theta(y-b)\right\} \left(g^{-1}\right)^\prime(y)\, y=\mathcal{L}^{-1}[f](y)$$
where $g^{-1}$ is the inverse function $g^{-1}(g(x))...
- 17.2k
8
votes
Accepted
LaplaceTransform works well with x[t], but doesn't recognize x[1][t], how to make it works for x[1][t]?
Obviously a bug. (If I guess it right, it's introduced in v12.2 together with this bug. ) v9.0.1 gives the desired result:
A possible fix is turning to the method mentioned here:
...
- 60.8k
8
votes
Accepted
How to let Mathematica return impulse or Dirac delta functions when computing integrals?
If you use Dirac or Heaviside functions explicitly in your expression, Mathematica figures out that you're working with generalized functions. Unfortunately, it doesn't always work the other way: ...
- 13.6k
7
votes
Calculate the Bromwich Integral (Inverse Laplace Transform)
This is decidedly not a general answer, but let's play a bit. If we do
...
- 22.6k
7
votes
Accepted
How to do continuous Fourier transform?
It looks like Mathematica can do this. Define something like this (I've simplified your version slightly)
...
- 16k
7
votes
Accepted
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