4. Solve the p.d.e, $\frac{\partial u}{\partial t}=\frac{\partial^{2} u}{\partial t^{2}}$ subject to: Initial condition: $u(x, 0)=4 X-4 X^{2}, 0 \leq x \leq 1$, Boundary conditions: $u(0, t)=(1, t)=0, t>0$. Take $\Delta x=h=0.2$ and $\Delta t=k=0.04$. Solve for two levels. 5. Solve using the LU - decomposition method, the system of equations $$ \begin{array}{1} X+y+z=1 4 x+3 y-z=6 W 3 X+5 y+3 z=4 \end{array} $$ CS.JG. 067