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votes
Accepted
Is is preferable to use a difference formula of higher order of accuracy for spatial derivat...
You could use the method of lines to solve this PDE. If you use an explicit finite difference method, you will need to take a rather small time step (${\mathcal O(\Delta x^3))}$ due to the $u_{xxx}$ …
1
vote
Accepted
Advice on numerical solution for 2D hyperbolic PDE with zero flux boundary conditions
The reason you don't get conservation is that you've used the product rule before discretizing, so conservation would require an exact cancellation of truncation errors in the different product terms …
1
vote
Finite difference for a highly nonlinear equation - The wind within the forest
As noted already in the comments, your boundary conditions seem off. Note that generically for a second-order BVP one expects to impose only two boundary conditions; you have 4.
Once you’re sure you …