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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: ...
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### 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 ...
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819 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 $h_t - [h^3(1-h)^3 \varepsilon h_\theta]_\theta$ = ...
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769 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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### 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
346 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 ...
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224 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 ...
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975 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: ...
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317 views

### Problems with solving PDEs

I am using NDSolve to solve the two equations: ...
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431 views

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### 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. ...
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