AbstractA popular approach for the modeling of adsorption phenomena is density‐functional theory (DFT). A new methodology described here is the first completely reliable technique for finding all solutions to the nonlinear equation systems arising in the lattice‐DFT modeling of adsorption in porous materials. The method is based on interval analysis, in particular on an interval Newton/generalized bisection algorithm, which provides a mathematical and computational guarantee that all solutions are enclosed. The method is demonstrated using a model, formulated using DFT for a confined lattice, of adsorption in slit‐like nanoscale pores. In addition to confirming solutions found previously, the method also found on several test problems a number of additional, previously unreported solutions.