In principle, if we start from a high redshift, then the initial guess of u$_{i,j,k}$ could be such that the initial value of χ in all the space is equal to the background value ¯ χ , because anyway at this time we expect this to be approx- imately true. For subsequent time steps we could use the solution for u$_{i,j,k}$ at the previous time step as our initial guess; if the time step is small enough then we do not ex- 

pect u to change significantly between consecutive times so that such a guess will be good enough for the iteration to converge fast. 

In practice, however, due to specific features and al- gorithm of the MLAPM code [32], the above procedure may be slightly different in details. 

