[vahidmech]

I want to solve implicit energy equation by using Thomas algorithm and approximate factorization so after 2nd order centered discretezation I have
(I+X(delta_time))(I+Y(delta_time))(delta_temperatu re)=((FI)^n+S^n)(delta_time)
where
delta_temperature=T^n+1-T^n
and other parameter are in attached file (in brief X and Y are operator that relate a cell value to neighbor cells in x and y direction respectively)
when I sweep in second direction my boundary condition is delta_temperature for ghost cell equal to delta_temperature for live boundary cell but I don not know what boundary condition I must use when I sweep in first direction?