内容摘要： 

We introduce a symmetric fractional-order reduction (SFOR) method to construct numerical algorithms on general nonuniform temporal meshes for semilinear fractional diffusion-wave equations. By using the novel order reduction method, the governing problem is transformed to an equivalent coupled system, where the explicit orders of time-fractional derivatives involved are all $\alpha/2$ $(1<\alpha<2)$. The linearized L1 scheme and Alikhanov scheme are then proposed on general time meshes. Under some reasonable regularity assumptions and weak restrictions on meshes, the optimal convergence is derived for the two kinds of difference schemes by energy method.

主讲人简介: 

吕品，西南财经大学数学学院副教授。2018年博士毕业于澳门大学数学系，主要研究方向为分数阶微分-积分方程的数值算法，特别是非均匀时间网格算法。目前已在J. Sci. Comput.、Numer. Algorithms、Appl. Numer. Math.、Appl. Math. Lett.、Comput. Math. Appl.等SCI期刊上发表20余篇论文，主持一项国家自然科学基金、一项四川省自然科学基金和多项中央高校基金，曾获“East Asia SIAM Student Paper Prize”和“澳门特别行政区研究生科技研发奖”。