Linked Questions
10 questions linked to/from Conservation of area solving a PDE via finite difference scheme
54
votes
4
answers
8k
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Dynamic Euler–Bernoulli beam equation
I am trying to solve for the vibration of a Euler–Bernoulli beam. The equation is
$\frac{\partial ^2u(t,x)}{\partial t^2}+\frac{\partial ^4u(t,x)}{\partial x^4}=0$
For the boundary conditions I ...
- 16.6k
25
votes
2
answers
3k
views
I failed to solve a set of one-dimension fluid mechanics PDEs with NDSolve
The fluid here has been assumed as single component perfect gas i.e. it obeys the equation $p=ρ R T$, the thermal conductivity is assumed as a constant, so the equation set is:
...
- 67.6k
20
votes
4
answers
3k
views
Symmetry-finding packages
Where can I find the most up-to-date or whatever you consider to be the most useful symmetry-finding package for differential equations? I do not intend to restrict to, but would like to include those,...
- 305
22
votes
2
answers
1k
views
NDSolve uses different difference order for different spatial derivative when solving PDE
I found something this tutorial for method of line doesn't tell us.
Consider the following toy example:
...
- 67.6k
19
votes
1
answer
2k
views
How to solve the tsunami model and animate the shallow water wave?
Backslide introduced in 9.0, persisting through 13.1.
Recently when I was learning differential equations, I noticed there is a shallow water wave equation to model the tsunami propagation.
How to ...
- 3,047
13
votes
2
answers
635
views
Nonlinear dispersal equation modeling insect aggregation
I'm a newbie with Mathematica, I know it's a basic answer, but I can't solve the problem on my own.
I have the following equation reflecting insect aggregation at low population densities (taken from ...
- 421
7
votes
1
answer
364
views
Instability, Courant Condition and Robustness about solving 2D+1 PDE
After several discussions, I would like to focus on the robustness of solving 2D+1 PDE by considering all suggested methods from @xzczd (see here)
I found that the Ratio between the convection term ...
- 445
5
votes
3
answers
323
views
5
votes
1
answer
327
views
How to solve a 2D+1 PDE with a large convection term in stable and efficient way
Follow from the discussion 2D+1 PDE problem
$\partial_t u(t,x,y)=-y\partial_{x}u+\partial_{y}\left[γ(1+sin(3x)) yu+A sin(3x)u+γkT(1+sin(3x))\partial_{y}u\right]$
with $u(0,x,y)=\frac{1}{2\pi}e^{-(x^...
- 445
4
votes
1
answer
225
views
Different results from NDSolve of v9 and v11
When using NDSolve to solve 2 pdes with different version of Mathematica, I obtained totally different results. The code is as follows.
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