Modify the following code to solve the diffusion equation withNeumann boundary conditions using finite differences.
![-t = u xx-ISK<l , with Neumann boundary conditions N-50 [D,x] cheb(N) D-D D2 D2; % initial condition u0- cos (pix) +0.2 cos (5 pi x)+1; % boundary conditions g2 B -D2 (2:end-1, [1 end] (t) 0 t+1 D2 D2 (2 end-1,2:end-1) AD(1,1) D(1,end)D(end,1 D(end, end) C [D (1,2:end-1D (end, 2:end-1) t 0:0.001:2; - [T,U- ode45 ( (t,u) D2u(B/A)gl (t) g2 (t)1-C*u), t, u0 (2:end-1) for k-2: length(t) S-expm(D2 t(k)u0 (2:end-1) plot (x (2:end-1),U(k, - ylim -1 2]) shg drawnow end](https://d2vlcm61l7u1fs.cloudfront.net/media%2F175%2F1752aa21-3573-4f9e-a786-e45f0cc40ce3%2FphpeEya7A.png)
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Modify the following code to solve the diffusion equation withNeumann boundary conditions using finite differences.
![-t = u xx-ISK<l , with Neumann boundary conditions N-50 [D,x] cheb(N) D-D D2 D2; % initial condition u0- cos (pix) +0.2 cos (5 pi x)+1; % boundary conditions g2 B -D2 (2:end-1, [1 end] (t) 0 t+1 D2 D2 (2 end-1,2:end-1) AD(1,1) D(1,end)D(end,1 D(end, end) C [D (1,2:end-1D (end, 2:end-1) t 0:0.001:2; - [T,U- ode45 ( (t,u) D2u(B/A)gl (t) g2 (t)1-C*u), t, u0 (2:end-1) for k-2: length(t) S-expm(D2 t(k)u0 (2:end-1) plot (x (2:end-1),U(k, - ylim -1 2]) shg drawnow end](https://d2vlcm61l7u1fs.cloudfront.net/media%2F175%2F1752aa21-3573-4f9e-a786-e45f0cc40ce3%2FphpeEya7A.png)
Need help!!
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