Solve heat equation  in  with conditions  using Crank-Nicolson method with  , upto two time steps.

To solve the heat equation \( u_{tt} = u_{xx} \) using the Crank-Nicolson method with the given conditions and parameters, we first discretize the domain and time, then apply the method iteratively to find the solution up to two time steps.

Let's denote \( u_{i,j} \) as the numerical approximation of \( u(x_i, t_j) \), where \( x_i = ih \) with \( h = 0.25 \) and \( t_j = j\lambda \) with \( \lambda = 1 \).

The Crank-Nicolson method discretizes the heat equation as:

\[ \frac{u_{i,j+1} - 2u_{i,j} + u_{i,j-1}}{\lambda^2} = \frac{1}{2} \left( \frac{u_{i+1,j+1} - 2u_{i,j+1} + u_{i-1,j+1}}{h^2} + \frac{u_{i+1,j} - 2u_{i,j} + u_{i-1,j}}{h^2} \right) \]

We rearrange this equation to solve for \( u_{i,j+1} _________ ___ _____ ____ ________ ______ __________ ___ ________.
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