报告题目：Numerical analysis for high-order methods for variable-exponent fractional diffusion-wave equation

报 告 人：邱文林，山东大学

报告摘要：This work considers the variable-exponent fractional diffusion-wave equation, which describes, e.g. the propagation of mechanical diffusive waves in viscoelastic media with varying material properties. Rigorous numerical analysis for this model is not available in the literature, partly because the variable-exponent Abel kernel in the leading term may not be positive definite or monotonic. We adopt the idea of model reformulation to obtain a more tractable form, which, however, still involves an“indefinite-sign, nonpositive-definite, nonmonotonic”convolution kernel that introduces difficulties in numerical analysis. We address this issue to design two high-order schemes and derive their stability and error estimate based on the proved solution regularity, with α(0)-order and second-order accuracy in time, respectively. Numerical experiments are presented to substantiate the theoretical findings.

报告人简介：邱文林，博士。2024年7月进入山东大学数学学院从事博士后研究，合作导师为郑祥成研究员。主要从事偏积分微分方程的理论与数值分析及变指标分数阶微分方程的数值分析与计算等方面的研究；近5年在《SIAM J. Multiscale Model. Simul.》、《Adv. Comput. Math.》、《J. Sci. Comput.》、《Fract. Calc. Appl. Anal.》、《Appl. Numer. Math.》等杂志发表SCI论文40余篇，其中ESI高被引论文5篇，Google学术引用量800余次。担任美国数学评论MR和德国数学文摘zbMATH评论员。目前主持国家资助博士后研究人员计划项目一项。

报告时间：2024年12月7日 16:30-17:30

报告地点：文渊楼B536

主办单位：数学与统计学院