Linked Questions
13 questions linked to/from Nonlinear dispersal equation modeling insect aggregation
22
votes
2
answers
1k
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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:
...
- 68.4k
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 ...
- 3,069
16
votes
2
answers
838
views
Conservation of area solving a PDE via finite difference scheme
I have two PDEs that describe the movement of fluid:
$h_t + [h^3(1-h)^3((1+\varepsilon h)\sin \theta - \varepsilon h_\theta \cos \theta]_\theta$ = 0
$h_t - [h^3(1-h)^3 \varepsilon h_\theta]_\theta$ = ...
- 723
7
votes
3
answers
2k
views
Time dependent Schrödinger equation in 2D
I have the following Schrödinger equation in $2D$:
\begin{cases}
\partial_t \Psi(x,t) = V(x,t) \Psi(x,t) \quad x \in [-10,10]^2\\
\Psi(x,0)=\exp( \frac{1}{2} (-x^2+y^2))
\end{cases}
where the ...
- 421
9
votes
2
answers
856
views
Numerically solving the KdV equation
Backslide introduced in 9, persisting through 13.
I am trying to solve the KdV equation numerically. The following code would work perfectly in version 5:
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- 243
4
votes
2
answers
466
views
Using NDSolveValue for Solving a parabolic PDE numerically
Inspired by this question I am trying to solve the following PDE numerically on $x \in [-3, 3]$ and $t \in [0, 0.5]$ using NDSolveValue:
$$
\frac{\partial p}{\partial t} = (12x^2-4) p + \left[4x(x^2-1)...
- 325
5
votes
1
answer
1k
views
PDE of real-world system, integral boundary condition
I've stripped all the physical-significance for clarity, but I know that u[x,t] will be everywhere positive and continuous.
here are the equations in Mathematica code:
...
- 487
7
votes
1
answer
372
views
Instability, Courant Condition and Robustness about solving 2D+1 PDE
After several discussions, I would like to focus on the robustness of solving 2D+1 PDE by considering all suggested methods from @xzczd (see here)
I found that the Ratio between the convection term ...
- 445
5
votes
3
answers
326
views
4
votes
1
answer
212
views
Steady state solution (1D) of nonlinear dispersal equation
Now I'm interested in the equation $$\frac{\partial }{\partial x}\Bigl(\text{sgn}(x) u \Big) +\frac{\partial}{\partial x} \Bigl[ u^2 \frac{\partial u}{\partial x} \Bigr] =0$$ with boundary conditions $...
- 421
6
votes
1
answer
253
views
I understand mol but meet difficulty in understanding how `pdetoode` atumatically generate pde-to-ode-rules by using this strange pattern and rule?
I often solve pdes for my research, and years ago I found pdetoode in this forum is very handy. Although it is a small piece of code, it solves several interesting ...
- 1,495
4
votes
1
answer
228
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.
...
- 823
3
votes
1
answer
144
views
Inactive[Grad] is lost when NDSolve parses PDE
I encountered this when trying to solve the PDE mentioned here. I've transformed the equation to the following:
...
- 68.4k