please help with both a and b$!!!$

$(20$ marks$)$ Heat Deduction Equation

Consider the following PDE from the heat deduction problem

$u_t=u_x$

$u(t,0)=0,u(t,1)=0$

$u(0,x)=-x^2+x$

a$).$ Provide the algorithm $($in pseudo$-$code$)$ for solving the PDE by the Crank$-$Niclson method.

b$).$ Implement the algorithm into Matlab code and plot $u(t,x)$ on the grid of $[0,1]=x$ with $M=N=50$ in constant steps.

Submit your Matlab Code.