报告人: 肖爱国教授 （湘潭大学）

报告题目: Conservative difference scheme for space fractional Klein- Gordon-Schrödinger equations with Yukawa interaction

报告摘要：In this paper, a conservative finite difference scheme is presented to solve space fractional Klein-Gordon-Schrödinger system with Yukawa interaction. In discretization, we apply the central finite difference scheme to spatial derivatives, the Crank-Nicolson and leap-frog schemes to Schrödinger and Klein-Gordon equations in time direction respectively. Our scheme can be decoupled and preserves mass and energy conservation laws. The existence, uniqueness and convergence of the scheme are proven, and it is shown that the scheme is of the space-time accuracy of order 2. The numerical experiments are given, and verify the correctness of theoretical results and the efficiency of the scheme. In particular, the effects of the fractional order α and high-degree term coefficients on the solution behaviors are examined, and some interesting physical phenomena including quantum subdiffusion and local oscillation are observed.

   The above works are finished by cooperation with Junjie Wang and Chuanxi Wang.

报告人简介：1999年在北京应用物理与计算数学研究所获博士学位；2001年从中国科学院数学与系统科学研究院博士后出站。现任湘潭大学数学与计算科学学院二级教授、国防科技数值算法与模拟湖南省国防科技重点实验室主任、科学工程计算与数值仿真湖南省重点实验室副主任。入选湖南省高校学科带头人。兼任中国仿真学会仿真算法专业委员会主任及三个国家学会理事、《计算数学》编委等。主要研究方向为微分方程数值方法，主持国家自然科学基金面上项目4项、国家863课题1项及部省项目8项；获教育部自然科学二等奖、国家教学成果二等奖、湖南省教学成果一等奖、宝钢教育奖等奖励；在J. Comput. Phys., J. Sci. Comput., Fract. Calcu. Appl. Anal., BIT 等权威期刊发表SCI论文60多篇，培养博、硕士40多名。

报告时间: 2017年6月7日（星期三）下午15:30-16:30

报告地点: 科技楼南楼702室