Can someone suggest whether we can safely use fndsdx function for finding derivatives for a steep function (such has having shocks), secondly is there any way in PHOENICS to find double derivative other than calling fndsdx twice?

My other question is, does phoenics takes nodes coinciding with boudary or it assumes cell wall matching the boundary? Why I am asking this question in PHOENICS, when using patch/ coval to fix the boundary value, gives different value of function, if I specify 100,25) in the last two places of coval funtion, which implies, the wall is set to 25 and node value is an interpolated value. There are 2 possibilities, wall at end with node interior by a distance of dxu2d or the wall is a fictitious outside boundary and node is matching the boundary. Please someone clarify.

My last question is, Is there any way to find the fluxes per unit time passing through the cell walls (faces) in a transient problem?

Thanks friends in advance for your help!

Sanjay

...in my last question, the fluxes across cell walls are mass fluxes to be computed for del t time. This value I want to use to update my boundary by doing mass balance beyond the computed domain.