Changes between Version 49 and Version 50 of u/bliu/pnfldiff


Ignore:
Timestamp:
09/04/18 16:42:07 (6 years ago)
Author:
Baowei Liu
Comment:

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  • u/bliu/pnfldiff

    v49 v50  
    5252== Discretize the equations ==
    5353
     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.
    5459
    5560