Linked Questions

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: ...

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 ...

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 ...

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 ...

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 $h_t - [h^3(1-h)^3 \varepsilon h_\theta]_\theta$ = ...

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)...

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 $\omega$-...

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 ...

Motivation As discussed here, NDSolve uses different difference orders for various spatial derivatives and the implicit design could cause trouble in certain cases....

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: ...

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 ...

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 ...

NDSolve can be broken into three stages: NDSolve`ProcessEquations processes the equations and sets up an NDSolve`StateData ...

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 ...

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 ...