Linked Questions
20 questions linked to/from Implement finite Fourier transforms
44
votes
4
answers
2k
views
Is there a convenient way to copy/paste text-interspersed SE code snippets into Mathematica?
Is there a way to copy and paste code snippets from SE to Mathematica if these snippets are interspersed with text?
Like e.g. in Morphing Graphics, color and location in both the question and answer, ...
- 15.5k
21
votes
4
answers
1k
views
What's wrong with this FFT-based Von Kármán vortex street simulation?
About 9 years ago, I came across this interesting website, and found the following paragraph with a broken Mathematica code sample:
When fluid passes an object, it can leave a trail of vortices ...
- 67.7k
14
votes
2
answers
2k
views
A more convenient Fourier series
Personally, I feel the design of FourierSeries/FourierSinSeries/FourierCosSeries/...
- 67.7k
7
votes
4
answers
617
views
What is wrong with my approach to solving a heat transfer PDE?
I wanna solve the following heat transfer PDE using Mathematica.
$\qquad u_{xx}=u_{t}$
with following conditions:
$\qquad
\begin{cases}u(x,0)=sin(x) &0<x<\pi &,t>0\\u_{x}(0,t)=1\\...
- 83
13
votes
1
answer
588
views
why can't Mathematica solve the wave PDE on string when adding a dispersion term?
Could someone possibly gives an insight as to why DSolve can solve
$$
\frac{\partial^{2}u}{\partial t^{2}}=\frac{\partial^{2}u}{\partial x^{2}
}\qquad t>0
$$
...
- 149k
7
votes
2
answers
909
views
Laplace PDE inside a disk
I can't get Mathematica to solve this standard textbook PDE, which is Laplace inside a disk of some radius. One of the boundary conditions needed is that the solution is finite (bounded) in center of ...
- 149k
3
votes
3
answers
892
views
Solve initial-boundary value problem of heat equation without NDSolve or DSolve
I want to solve the following pde
pde = D[u[t, x], t] - D[u[t, x], x, x] == 0
with the boundary conditions defined as
...
- 31
7
votes
1
answer
438
views
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
...
- 27.8k
2
votes
2
answers
666
views
Laplace's equation with mixed boundary condition using separation of variables
The equation and boundary condition are defined in the picture where $T_1$, $T_2$, $T_3$, $k$ and $h$ are constant value.
I am trying to use variable separation to solve the problem.
If $T(x,y)$ ...
- 23
1
vote
2
answers
498
views
How to obtain the exact solution of a partial differential equation?
I know that Mathematica can solve a PDE numerically, but I wonder if it is possible to obtain the exact solution. For example, consider the heat equation
$$u_t = \kappa u_{xx} $$
Is it possible to ...
- 11
8
votes
2
answers
366
views
Two-dimensional Laplacian coupled with another equation leading to a BVP with integral bc(s)
I have the two-dimensional Laplacian $(\nabla^2 T(x,y)=0)$ coupled with another equation. The Laplacian is defined over $x\in[0,L], y\in[0,l]$. On manipulating the second equation (which I have ...
- 297
3
votes
1
answer
727
views
Inverse Laplace transform of this complicated function
I have been solving a coupled PDE system analytically and I need to find the inverse Laplace transform of $(1)$ and get $T(x,y)$. $s$ is the Laplace domain variable and $\alpha, \beta, \gamma, T_{fi}, ...
- 297
2
votes
2
answers
1k
views
Comparing analytical solution with numerical solution of Helmholtz equation in a unit square
I am just learning PDE, and I am interested to compare analytical solution with numerical solution of Helmholtz equation in a unit square with zero boundary condition. I am not sure if it possible. ...
- 91
2
votes
2
answers
316
views
Symbolic solution for Laplace equation with pure Neumann b.c. and constraint at a point
Starting problem:
$$
\begin{cases}
\nabla^2 f = 0 & \text{on} \; \Omega \\
\frac{\partial}{\partial\mathbf{n}} f = y\,n_x - x\,n_y & \text{on} \; \partial\Omega
\end{cases}
$$
with $\Omega \...
- 4,452
5
votes
1
answer
393
views
how to obtain solution for $u_t+u=u_{xx}$
I was trying to verify my hand solution for this PDE using Mathematica.
Is a trick to help Mathematica obtain solution to $u_{t}+u=u_{xx}$ with initial conditions $u(x,0)=f(x)$ and boundary ...
- 149k
1
vote
3
answers
150
views
DSolve returns no result
I'd like to solve a partial differential equation on a infinite strip. My code is the following:
...
- 407
3
votes
1
answer
247
views
Symbolic solution for steady-state heat equation i.e. Laplace equation inside cylinder
I want to symbolically solve the following boundary value problem in my textbook. It's steady-state heat conduction equation i.e. Laplace equation inside a cylinder
$$
\left\{\begin{array}{l}
\Delta u=...
- 1,582
3
votes
1
answer
687
views
Solving a BC Differential equation, (Buckling) any way possible
I am trying to verify my manual solution for this problem by any way, so I tried NDSolve, and DSolve, with no success.
Can some one help, or even give me the final numbers :D
I need the first 3 ...
- 93
1
vote
1
answer
319
views
Fourier Series of ODE
I am having trouble finding the Fourier series of a 2nd order ODE. Should I be using the piecewise function as well to set up the range for t?
Solve $ y'' + \omega^2 𝑦 = r(t) $, where $ r(t) = |t|, -\...
1
vote
0
answers
315
views
Solving a heat equation problem(DSolve)
I'm brand new to Mathematica. I am trying to solve a heat equation problem, but I keep getting back the input on the output line.
The problem:
In:
...
- 11