The suggested solutions was what I derived by working out the Pde but I need help with the implementation for rest of the questions. I have little experience in coding.

Ut + Up = 0, 2 (0,21],t> 0, u(1,0) = sin(2.1). Assume periodic boundary conditions. Write down the exact solution Utrue(1, t) of the PDE. Suggested solution Utrue(x, t) = -sin(2t - 2.) Derive a Fourier-Collocation approximation scheme in space. Suggested Solution Assume un(x, t) = my n(t)exp(int) then from class we deduce that 3 [ality ini.] erpline;) = 0 - inn exp(inr) = 0 in/ 0, u(1,0) = sin(2.1). Assume periodic boundary conditions. Write down the exact solution Utrue(1, t) of the PDE. Suggested solution Utrue(x, t) = -sin(2t - 2.) Derive a Fourier-Collocation approximation scheme in space. Suggested Solution Assume un(x, t) = my n(t)exp(int) then from class we deduce that 3 [ality ini.] erpline;) = 0 - inn exp(inr) = 0 in/