Here is some code I have written to solve the evolution equation:

film_evol_3.m   % this function solves the problem with boundary conditions h=h_b, h_xxx+alpha =0 at x=0, and h_x=0, h_xx=delta at x=1

soln_plot.m  % plots the film profile at a given snapshot in time

soln_movie.m  % creates a movie of the evolution of the film over a given time range

Here is a typical call to these functions:

N=50;

H=.08*ones(1,N);

H(1)=.09; H(50)=.09;

alpha=-50;  % magnetic force stronger than gravity

h_b=.1;  % fixed boundary condition at the top

delta=2;  % the fixed value of the curvature at the bottom

[t,h,X]=film_evol_3(alpha, h_b, delta, N, 15, H);

M=soln_movie(X,h,2,length(t));

A few notes:

• The problem being solved is for a tangentially immobile surface, primarily because that is the easiest
• I have not been real careful with scaling and dimensionless constants, etc.  These details are easy to implement in the code, however.
• Different boundary conditions are fairly easy to implement in the code.  Changes can be made by altering the assignments of hneg1, h0, hNplus1, and hNplus2 (h0, hNplus1 are the boundary grid points, hneg1, hNplus2 are fictitious points

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