Linked Questions
15 questions linked to/from NDSolve uses different difference order for different spatial derivative when solving PDE
23
votes
2answers
2k 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:
...
13
votes
3answers
986 views
Time evolution/dynamics of circular plate with hole (Biharmonic equation and stiffness)
On this Mathematica.SE form, there exists information on how to use Mathematica to demonstrate the vibration of a circular membrane and the deflection of an orifice plate (the latter I had raised ...
17
votes
1answer
1k views
How to solve the tsunami model and animate the shallow water wave?
Backslide introduced in 9.0, persisting through 11.3.
Recently when I was learning differential equations, I noticed there is a shallow water wave equation to model the tsunami propagation.
How to ...
11
votes
2answers
409 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 ...
15
votes
2answers
679 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
$h_t - [h^3(1-h)^3 \varepsilon h_\theta]_\theta$ = ...
2
votes
2answers
351 views
Unstable solution of 2D+1 time PDE with periodic boundary condition
Now I am trying to solve the following 2D+1 type of PDE:
$\partial_t u(t,x,y)=-y\partial_{x}u+\partial_{y}\left[a y+b sin(x)u+c\partial_{y}u\right]$
with $u(0,x,y)=\frac{1}{2\pi}e^{-((x-\pi/4)^2+y^2)...
2
votes
2answers
381 views
Solving 2D+1 PDE with Pseudospectral in one direction with periodic boundary condition?
According to the documentation about the pseudospectral difference-order:
It says:
Following the discussion here:
I found the messy behavior is always on the artificial boundary in $\omega$-...
7
votes
1answer
269 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 ...
8
votes
1answer
535 views
Solve PDEs with finite difference scheme by modifying NDSolve-based solver
Motivation
As discussed here, NDSolve uses different difference orders for various spatial derivatives and the implicit design could cause trouble in certain cases....
4
votes
1answer
393 views
WorkingPrecision in NDSolve causes failure when solving a simple PDE
I have fivefold multiple integral and I wanted a speed calculations. I came across on this Question and had already begun the problems.
Here is a toy example with simple double integral:
...
4
votes
2answers
168 views
MoL: How to enforce Chebyshev–Gauss–Lobatto points in SpatialDiscretization?
In Mathematica documentation one is prompted to use a grid with points at the zeros of the Chebyshev polynomials so that Runge's phenomena arising from ...
3
votes
1answer
209 views
Singularities forming on boundary while solving system of pde's
Backslide introduced after 9.0.1, fixed in 12.0.1 or earlier.
This is a follow up of a previous question I asked regarding solving a system of coupled, non-linear partial differential equations, 2D ...
8
votes
1answer
129 views
Can we construct our own NDSolve`StateData?
NDSolve can be broken into three stages:
NDSolve`ProcessEquations processes the equations and sets up an NDSolve`StateData ...
9
votes
0answers
123 views
How to modify NDSolve`StateData without crashing the kernel?
Probably a hard question, but it's better to cry out loud.
Reminded by Chris K, I noticed my fix function has been broken since v11.3. After some checking, I ...
2
votes
1answer
156 views
Fixing the difference order for space derivatives in a PDE when using NDSolve
I am trying to implement the fix to make the difference order uniform for all space derivatives in a PDE, as described in this post: NDSolve uses different difference order for different spatial ...