Crank-nicolson method, MATLAB Programming

Assignment Help:

 

clear

tic

L=1;

T=0.2;

nust=2000;

dt=T/nust;

n=40;

dx=L/n;

 

r=1;

 omega=10:10:5000;%Store Range of Frequencies for Simulation

u=zeros(n+1,nust+1);%Initialize the grid (Space along rows/dim1& time along cols/dim2)

% Bar Boundary Condition

time=zeros(1,nust+1);%Time Elapsed Vector

for k=1:nust+1

u(1,k)=0;

u(n+1,k)=0;

time(k)=(k-1)*dt;

end

% Bar Initial Condition

x=zeros(n+1,1);%Length Vector

fori=1:n+1

x(i)=(i-1)*dx;

u(i,1)=sin(pi*x(i));

end

%constructing the Matrix in the right side

ar(1:n-2)=r;

br(1:n-1)=2-2*r;

cr(1:n-2)=r;

Mr=diag(br,0)+diag(ar,-1)+diag(cr,1);

 

%constructing the Matrix in the left side

al(1:n-2)=-r;

bl(1:n-1)=2+2*r;

cl(1:n-2)=-r;

Ml=diag(bl,0)+diag(al,-1)+diag(cl,1);

%aa=Ml\Mr;

 

% Crank Nicolson Implementation

u_sol=zeros(length(u(:,1)),length(u(1,:)),length(omega));

forll=1:length(omega)

for k=2: nust

        C=0.5*dt*(cos(omega(ll)*k*dt)+cos(omega(ll)*(k+1)*dt))*ones(length(2:n),1);

uu=u(2:n,k-1);

        u(2:n,k)=inv(Ml)*((Mr*uu)+C);

end

u_sol(:,:,ll)=u;

    clear uu;

end

 

figure;

subplot(2,1,1); mesh(x,time,u_sol(:,:,1)')

title(['Solution for omega=',num2str(omega(1))]);

subplot(2,1,2); mesh(x,time,u_sol(:,:,end)')

title(['Solution for omega=',num2str(omega(end))]);

xlabel('x-axis');

ylabel('Temperature');

toc

The code you have provided me at that time was giving the out of the whole process( as a plot ) which isgood but we cannot specify a point in the rod to find the temperature , for example if we need to know the temperature at the distance 0.5 ( we know the total length is 1) there is no way to get it . so what I need is the following :

We have a rod with a length of 1 and we want to know the temperature at the center of the rod ( we may change the point we want to know ) and the output must be a number not a plot , I mean I want the MATLAB to tell me the temperature at the specified point.


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