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This is a classic heat equation problem with boundary conditions. The problem is: \[ u_t = u_{xx}, \quad 0 < x < l, \quad t > 0 \] with the boundary conditions: \[ u(0, t) = u(l, t) = 0 \] and the initial condition: \[ u(x, 0) = x(l - x), \quad 0 \leq x \leq l \] To solve this numerically, we can use a method like finite difference, which discretizes the equation and solves it step by step in both space and time. ### Steps: 1. Discretize the domain: - Discretize space with step size \( \Delta x \), so \( x_i = i \Delta x \) for \( _________ _____ ______ _______ __________ ______ _____ _______.
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