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I'm using a finite differencing scheme to solve the following $$h_t = h h_{zz} + 2h_z^2$$ where the subscripts denote partial derivatives. The difficulty I'm facing is the boundary conditions are dynamic, and move with time ##t##. This makes choosing a ##\Delta z## very difficult and unintuitive for me.

I have already developed a MatLab code that works pretty well but I feel my ##\Delta z## should change in time. If anyone knows any references or has advice on this issue of dealing with the ##\Delta z## please let me know.

Thanks so much!

Josh

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# Finite Differencing Dynamic Boundary

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