Question: with initial data u(0,x) = exp( -x^2) and periodic boundary condition in x. i) Write down a Fourier (spectral) numerical scheme for this equation. Implement

with initial data u(0,x) = exp( -x^2) and periodic boundary condition

with initial data u(0,x) = exp( -x^2) and periodic boundary condition in x.

i) Write down a Fourier (spectral) numerical scheme for this equation. Implement this scheme in Matlab and solve up to t = 20.

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