  This paper concerns the numerical solution of three-dimensional degenerate
Kawarada equations. These partial differential equations possess highly
nonlinear source terms, and exhibit strong quenching singularities which pose
severe challenges to the design and analysis of highly reliable schemes.
Arbitrary fixed nonuniform spatial grids, which are not necessarily symmetric,
are considered throughout this study. The numerical solution is advanced
through a semi-adaptive Local One-Dimensional (LOD) integrator. The temporal
adaptation is achieved via a suitable arc-length monitoring mechanism. Criteria
for preserving the positivity and monotonicity are investigated and acquired.
The numerical stability of the splitting method is proven in the von Neumann
sense under the spectral norm. Extended stability expectations are proposed and
investigated.
