On a Nonuniform Crank-Nicolson Scheme for Solving the Stochastic Kawarada Equation via Arbitrary Grids

Abstract

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.

22 pages, 19 figures, 1 table, article is already accepted (author is uploading to arXiv to centralize all papers)

References in corpus (1)

• On the positivity, monotonicity, and stability of a semi-adaptive LOD method for solving three-dimensional degenerate Kawarada equations

Cited by in corpus (3)

• The quenching of solutions to time-space fractional Kawarada problems
• Numerical solution of degenerate stochastic Kawarada equations via a semi-discretized approach
• A positivity- and monotonicity-preserving nonlinear operator splitting approach for approximating solutions to quenching-combustion semilinear partial differential equations