Check the file: Questions.pdf

**Subject Mathematics MATLAB for Mathematics**

Check the file: Questions.pdf

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Problem 1:

T=1;

n=100;m=10;

dt=T/n;

xmin=-1; xmax=1;

dx=2/m;

t=0:dt:T; x=-1:dx:1;

U=zeros(m+1,n+1);

U(:,1)=2*x'+1;

U(1,:)=-ones(n+1,1);

U(m+1,:)=3*ones(n+1,1);

alpha=dt/dx^2;

% d1=diag(ones(1,m-1));d2=diag(ones(1,m-2),1)...

% +diag(ones(1,m-2),-1);

% A=(1+alpha)*d1-0.5*alpha*d2;

% B=(1-alpha)*d1+0.5*alpha*d2;

A=(1+alpha)*diag(ones(1,m-1))-0.5*alpha*diag(ones(1,m-2),1)...

-0.5*alpha*diag(ones(1,m-2),-1);

B=0.5*alpha*(-2*diag(ones(1,m-1))+diag(ones(1,m-2),1)...

+diag(ones(1,m-2),-1));

inv(A)

for k=1:n...

T=1;

n=100;m=10;

dt=T/n;

xmin=-1; xmax=1;

dx=2/m;

t=0:dt:T; x=-1:dx:1;

U=zeros(m+1,n+1);

U(:,1)=2*x'+1;

U(1,:)=-ones(n+1,1);

U(m+1,:)=3*ones(n+1,1);

alpha=dt/dx^2;

% d1=diag(ones(1,m-1));d2=diag(ones(1,m-2),1)...

% +diag(ones(1,m-2),-1);

% A=(1+alpha)*d1-0.5*alpha*d2;

% B=(1-alpha)*d1+0.5*alpha*d2;

A=(1+alpha)*diag(ones(1,m-1))-0.5*alpha*diag(ones(1,m-2),1)...

-0.5*alpha*diag(ones(1,m-2),-1);

B=0.5*alpha*(-2*diag(ones(1,m-1))+diag(ones(1,m-2),1)...

+diag(ones(1,m-2),-1));

inv(A)

for k=1:n...

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