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

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 ...
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....
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: ...
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 ...
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 ...
129 views

### Can we construct our own NDSolveStateData?

NDSolve can be broken into three stages: NDSolveProcessEquations processes the equations and sets up an NDSolveStateData ...