English

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

Numerical Analysis 2024-12-20 v1 Numerical Analysis

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.

Keywords

Cite

@article{arxiv.1901.06365,
  title  = {On a Nonuniform Crank-Nicolson Scheme for Solving the Stochastic Kawarada Equation via Arbitrary Grids},
  author = {Joshua L Padgett and Qin Sheng},
  journal= {arXiv preprint arXiv:1901.06365},
  year   = {2024}
}

Comments

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