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This article 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. © 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1305–1328, 2017

Nonuniform Crank‐Nicolson scheme for solving the stochastic Kawarada equation via arbitrary grids