How can I solve two related non-linear equations using EDP finite volume method?

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zaynab
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Hi evryone,
the system i am working on, is composed of two relatied non-linear equations that I discretised using finite volume method with fully implicit scheme, the difficulty is that the two unknonw appear in both equations and i don't know how to solve it.

upload_2015-3-30_16-31-25.png


Any propositions?
Thank you.
 
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Sorry, i corrected the system:
upload_2015-3-30_17-42-19.png
 

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