Linked Questions

44 votes
4 answers

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, ...
2 votes
2 answers

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 \...
21 votes
4 answers

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 ...
3 votes
1 answer

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 vote
0 answers

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: ...
7 votes
1 answer

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 ...
0 votes
1 answer

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|, -\...
2 votes
2 answers

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 $T(x,y)$ ...
8 votes
2 answers

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 ...
7 votes
4 answers

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\\...
7 votes
2 answers

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 ...
1 vote
3 answers

DSolve returns no result

I'd like to solve a partial differential equation on a infinite strip. My code is the following: ...
3 votes
1 answer

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}, ...
1 vote
2 answers

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 ...
13 votes
1 answer

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 $$ \frac{\partial^{2}u}{\partial t^{2}}=\frac{\partial^{2}u}{\partial x^{2} }\qquad t>0 $$ ...

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