  In recent years, there has been a large increase in interest in numerical
algorithms which preserve various qualitative features of the original
continuous problem. Herein, we propose and investigate a numerical algorithm
which preserves qualitative features of so-called quenching combustion partial
differential equations (PDEs). Such PDEs are often used to model solid-fuel
ignition processes or enzymatic chemical reactions and are characterized by
their singular nonlinear reaction terms and the exhibited positivity and
monotonicity of their solutions on their time intervals of existence. In this
article, we propose an implicit nonlinear operator splitting algorithm which
allows for the natural preservation of these features. The positivity and
monotonicity of the algorithm is rigorously proven. Furthermore, the
convergence analysis of the algorithm is carried out and the explicit
dependence on the singularity is quantified in a nonlinear setting.
