报告题目 (Title)：A semi-discrete finite difference method for simulating two-sided space fractional convection-diffusion quenching problems（模拟双边空间分数阶对流扩散方程quenching问题的半离散有限差分格式）
报告人 (Speaker)：朱琳 教授（宁夏大学数学统计学院）
报告时间 (Time)：2026年5月22日（周五）14:00
报告地点 (Place)：校本部GJ303
邀请人(Inviter)：李常品、蔡敏
主办部门：理学院数学系
报告摘要：We investigate quenching solutions of an one-dimensional, two-sided Riemann-Liouville fractional order convection–diffusion problem. Fractional order spatial derivatives are discretized using weighted averaging approximations in conjunction with standard and shifted Grünwald formulas. The advective term is handled utilizing a straightforward Euler formula, resulting in a semi-discretized system of nonlinear ordinary differential equations. The conservativeness of the proposed scheme is rigorously proved and validated through simulation experiments. The study is further advanced to a fully discretized, semi-adaptive finite difference method. Detailed analysis is implemented for the monotonicity, positivity and stability of the scheme. Investigations are carried out to assess the potential impacts of the fractional order on quenching location, quenching time, and critical length. The computational results are thoroughly discussed and analyzed, providing a more comprehensive understanding of the quenching phenomena modeled through two-sided fractional order convection-diffusion problems.
