Linked Questions

54 votes
4 answers
8k views

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 ...
Hugh's user avatar
  • 16.4k
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: ...
xzczd's user avatar
  • 66k
19 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,...
Cameron Smith's user avatar
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: ...
xzczd's user avatar
  • 66k
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 ...
LCFactorization's user avatar
13 votes
2 answers
623 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 ...
Vefhug's user avatar
  • 421
7 votes
1 answer
346 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 ...
Bob Lin's user avatar
  • 445
5 votes
3 answers
317 views

Problems with solving PDEs

I am using NDSolve to solve the two equations: ...
user55777's user avatar
  • 671
5 votes
1 answer
321 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^...
Bob Lin's user avatar
  • 445
4 votes
1 answer
224 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. ...
Nobody's user avatar
  • 823