Linked Questions

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, ...
Yves Klett's user avatar
  • 15.4k
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 ...
xzczd's user avatar
  • 66.2k
14 votes
2 answers
1k views

A more convenient Fourier series

Personally, I feel the design of FourierSeries/FourierSinSeries/FourierCosSeries/...
xzczd's user avatar
  • 66.2k
7 votes
4 answers
603 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\\...
Moreza7's user avatar
  • 83
13 votes
1 answer
579 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 $$ \frac{\partial^{2}u}{\partial t^{2}}=\frac{\partial^{2}u}{\partial x^{2} }\qquad t>0 $$ ...
Nasser's user avatar
  • 143k
7 votes
2 answers
877 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 ...
Nasser's user avatar
  • 143k
3 votes
3 answers
890 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 ...
Daniel's user avatar
  • 31
7 votes
1 answer
428 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 ...
user64494's user avatar
  • 26.3k
2 votes
2 answers
640 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 $T(x,y)$ ...
Mulang Song's user avatar
1 vote
2 answers
480 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 ...
Kiera's user avatar
  • 11
8 votes
2 answers
360 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 ...
Avrana's user avatar
  • 297
3 votes
1 answer
684 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}, ...
Avrana's user avatar
  • 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. ...
Lila's user avatar
  • 91
2 votes
2 answers
300 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 \...
πρόσεχε's user avatar
5 votes
1 answer
370 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 ...
Nasser's user avatar
  • 143k
1 vote
3 answers
143 views

DSolve returns no result

I'd like to solve a partial differential equation on a infinite strip. My code is the following: ...
fasdgr's user avatar
  • 407
3 votes
1 answer
231 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=...
我心永恒's user avatar
  • 1,562
3 votes
1 answer
671 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 ...
Aladdin's user avatar
  • 93
0 votes
1 answer
284 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|, -\...
Mord Fustang199's user avatar
1 vote
0 answers
305 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: ...
rededx's user avatar
  • 11