I know the theta method is
$ u_{j}^{n+1} = u_{j}^{n} = (1+ \theta) r \delta x^{2} [u_{j}^{n}] + \theta r \delta x^{2} [u_{j}^{n+1}]$
However I am not sure how to prove that the above equation for the PDE
I know the theta method is
$ u_{j}^{n+1} = u_{j}^{n} = (1+ \theta) r \delta x^{2} [u_{j}^{n}] + \theta r \delta x^{2} [u_{j}^{n+1}]$
However I am not sure how to prove that the above equation for the PDE
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