function [x,rho_bar,rho,t_vec,rho_max,x_cl_vec,xi,t_vec1,Mr,Mr_scaled,D2]=integrate_ge2(t_final) %************************************************************************** % integreate_ge2.m % Solves the regularized gradient-energy equation for a thin-film flow. % Single-droplet initial condition. %************************************************************************** % Physical parameters: alpha=0.05; %************************************************************************** % Numerical parameters: N=1000; L=2*pi; dx=L/N; dt=1e-2; n_timesteps=t_final/dt; n_capture=10; %************************************************************************** % Initial conditions and potential function: x=(-L/2):dx:((L/2)-dx); x=x.'; rr=0.5; vol=1; aa=(3/4)*(vol/rr^3); h0=0*x; for i=1:length(x) if(abs(x(i))