Linked Questions

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
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
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
7 votes
1 answer
429 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
  • 26.4k
0 votes
1 answer
285 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
2 votes
2 answers
642 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
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
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
1 vote
0 answers
306 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
3 votes
1 answer
686 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
7 votes
4 answers
604 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
1 vote
2 answers
483 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
13 votes
1 answer
580 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
  • 144k
7 votes
2 answers
885 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
  • 144k
5 votes
1 answer
377 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
  • 144k

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