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An efficient method for time non-local Allen–Cahn equation
时间:2025年06月26日 17:40 点击数:

报告人:张国宇

报告地点:腾讯会议ID: 519540325

报告时间:2025年06月26日星期四21:30-22:00

邀请人:数学与统计学院

报告摘要:

The shifted non-local trapezoidal rule (SFTR) with a special shift is adopted to construct a finite difference scheme for the time non-local Allen-Cahn equation. Some essential key properties of the weights of SFTR are explored for the first time. Based on these properties, we demonstrate the discrete energy decay property and maximum-principle preservation for the scheme. Numerical investigations show that the scheme can resolve the intrinsic initial singularity of such nonlinear non-local equations on uniform meshes without any correction. Comparison with the classic non-local BDF2 and L2-1 method further validates the superiority of SFTR in solving the problem. Experiments concerning both discrete energy decay and discrete maximum-principle also verify the correctness of the theoretical results.

主讲人简介:

张国宇,内蒙古大学副教授,研究方向为微分方程数值解法及其应用,主持国家自然科学基金青年基金项目一项、内蒙古自治区自然科学基金项目一项。在Journal of Scientific Computing等期刊发表SCI论文数篇。

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