differential equations - Looking for examples of numerically solving coupled PDE and ODE

I am about to solve a system of coupled PDE and ODE in thermodynamics. My system is a bit complicated, so I would like to learn from some examples before coding my own system.

I searched this site and found several cases as following

Solving coupled PDE and ODE

Couple a PDE and ODE in NDSolve

And I would like to know if there are more of them, with topic like "Solving coupled PDE and ODE numerically".

If you know a good example, please post its link, and I would appreciate your help.

Answer

Here are six more (too many for a comment):

NDSolve: Couple ODE and PDE

NDSolve two PDE plus one ODE, together

NDSolve a system of one PDE coupled with an ODE

Simulating a combination of PDEs and ODEs

PDE: Specify AccuracyGoal, StepSize, and WorkingPrecision interval-wise

Unfortunately, most do not have answers.

Comments

plotting - Plot 4D data with color as 4th dimension

I have a list of 4D data (x position, y position, amplitude, wavelength). I want to plot x, y, and amplitude on a 3D plot and have the color of the points correspond to the wavelength. I have seen many examples using functions to define color but my wavelength cannot be expressed by an analytic function. Is there a simple way to do this? Answer Here a another possible way to visualize 4D data: data = Flatten[Table[{x, y, x^2 + y^2, Sin[x - y]}, {x, -Pi, Pi,Pi/10}, {y,-Pi,Pi, Pi/10}], 1]; You can use the function Point along with VertexColors . Now the points are places using the first three elements and the color is determined by the fourth. In this case I used Hue, but you can use whatever you prefer. Graphics3D[ Point[data[[All, 1 ;; 3]], VertexColors -> Hue /@ data[[All, 4]]], Axes -> True, BoxRatios -> {1, 1, 1/GoldenRatio}]

plotting - Filling between two spheres in SphericalPlot3D

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plotting - Mathematica: 3D plot based on combined 2D graphs

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