How to solve Fick's second law of diffusion (second order differential in space and first order in time ) for a ternary or higher order systems?

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For a binary system Fick's second law can be solved, using Crank-Nicholson scheme followed by Gauss elimination and substitution (Thomas Algorithm).



However, for a ternary system, there will be two components (C1 and C2) involved in one equation and two such equations at every space step. How to proceed for this problem since tridiagonalisation won't work here?




differential-equations numerical-methods finite-differences finite-difference-methods




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    For a binary system Fick's second law can be solved, using Crank-Nicholson scheme followed by Gauss elimination and substitution (Thomas Algorithm).



    However, for a ternary system, there will be two components (C1 and C2) involved in one equation and two such equations at every space step. How to proceed for this problem since tridiagonalisation won't work here?




    differential-equations numerical-methods finite-differences finite-difference-methods




    share|cite|improve this question























      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      For a binary system Fick's second law can be solved, using Crank-Nicholson scheme followed by Gauss elimination and substitution (Thomas Algorithm).



      However, for a ternary system, there will be two components (C1 and C2) involved in one equation and two such equations at every space step. How to proceed for this problem since tridiagonalisation won't work here?




      differential-equations numerical-methods finite-differences finite-difference-methods




      share|cite|improve this question













      For a binary system Fick's second law can be solved, using Crank-Nicholson scheme followed by Gauss elimination and substitution (Thomas Algorithm).



      However, for a ternary system, there will be two components (C1 and C2) involved in one equation and two such equations at every space step. How to proceed for this problem since tridiagonalisation won't work here?





      differential-equations numerical-methods finite-differences finite-difference-methods





      share|cite|improve this question












      share|cite|improve this question




      share|cite|improve this question








      edited Jul 31 at 7:56









      mathreadler

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      13.5k71857









      asked Jul 31 at 6:25









      Aparna Tripathi

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