  This paper studies a nonuniform finite difference method for solving the
degenerate Kawarada quenching-combustion equation with a vibrant stochastic
source. Arbitrary grids are introduced in both space and time via adaptive
principals to accommodate the uncertainty and singularities involved. It is
shown that, under proper constraints on mesh step sizes, the positivity,
monotonicity of the solution, and numerical stability of the scheme developed
are well preserved. Numerical experiments are given to illustrate our
conclusions.
