Changes between Version 49 and Version 50 of u/bliu/pnfldiff
- Timestamp:
- 09/04/18 16:42:07 (6 years ago)
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u/bliu/pnfldiff
v49 v50 52 52 == Discretize the equations == 53 53 54 $I^{n+1}_{i}+\Delta t \phi (D_{i}^{n+1}(I,n_{H})+L_{I,i}^{n+1}(I,n_{H}))=I^{n}_{i}+\Delta t (\phi -1) (D^{n}_{i}(I,n_{H})+L_{I,i}^{n}(I,n_{H})$ 55 $n_{H,i}^{n+1}+\Delta t\phi L^{n+1}_{n_{H},i}(I, n_{H})=n_{H,i}^{n}+\Delta t(\phi -1) L^{n}_{n_{H},i}(I,n_{H})$ 56 $e_{i}^{n+1}+\Delta t\phi L^{n+1}_{e,i}(I,n_{H})=e_{i}^{n}+\Delta t (\phi -1) L^{n}_{e,i}(I,n_{H})$ 57 58 $\phi=1$ for backward Euler method and $\phi=1/2$ for Crank-Nicolson method. 54 59 55 60