Hi !

I am solving analytically the Jacobian of reaction ODE in order to compare with my numerical results. I used the theorie of Frederico perini in which he emits an approximation of the derivative of the reaction rate of progress as a ( stoechiometric matrix of reactant * rate of progress of reactant - stoechiometric matrix of product* rate of progress of product) / (mass fraction species ).

Through this formula we can see that if a species has a mass fraction equal to zero, it will not work for that species . In his paper, he did not detail in which conditions the approximation is valid.

Thus, what i did, i considered for that specie if mass fraction is equal to zero then i put directly zero on the derivative matrix box, but this has a great impact on my jacobian result. Asuming a( i, j ) is the jacobian obtained, then it forces all matrix box for which y(j)=0, to contain zero.

Could someone tell me how can i use the perini frederico approximation for zero mass fraction and if it only work when all mass fraction of species are greater than zero ?

Thanks you,