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With a correction term Forward Euler becomes Crank-Nicolson

Use the other alternative u=au: u=au12aΔtu(1+12aΔt)u=au. Apply Forward Euler: (1+12aΔt)un+1unΔt=aun, which after some algebra can be written as un+1=112aΔt1+12aΔtun. This is a Crank-Nicolson scheme (of second order)!

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