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求解二维Allen-Cahn方程的保正隐式差分格式
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Abstract:
本文研究求解二维Allen-Cahn方程的保正隐式差分格式。通过证明得到当网格比满足
时，差分解具有保正性，且在无穷范数意义下有
的收敛阶，最后数值实验表明数值结果与理论结果相吻合。
In this paper, we study the positive-preserving implicit difference scheme for solving two-dimensional Allen-Cahn equation. It is proved that when the grid ratio satisfies
, the difference solution is positive-preserving and has the convergence order of
in the sense of infinite norm. Finally, numerical experiments show that the numerical results are consistent with the theoretical results.
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