EDP finite volume solving

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1. Mar 30, 2015

zaynab

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.

Any propositions?
Thank you.

2. Mar 30, 2015

zaynab

Sorry, i corrected the system: