报告题目：A linearized finite difference/spectral-Galerkin scheme for multi-dimensional distributed-order time-space fractional nonlinear reaction-diffusion-wave equation
报告时间：2019年11月28日（周四）下午3:00-4:30
报告地点：曲江校区hbs02红宝石线路报告厅教九楼9-617
摘要：In this talk, we present a linearized finite difference/spectral-Galerkin scheme for one-, two-, and three-dimensional distributed-order time-space fractional nonlinear reaction-diffusion-wave equation. By using Gauss-Legendre quadrature rule to discretize the distributed integral terms in both the spatial and temporal directions, we first approximate the original distributed-order fractional problem by the multi-term time-space fractional differential equation. Then, we employ the finite difference method for the discretization of the multi-term Caputo fractional derivatives and apply the Legendre-Galerkin spectral method for the spatial approximation. The main advantage of the proposed scheme is that the implementation of the iterative method is avoided for the nonlinear term in the fractional problem. Moreover, we present the stability analysis of the scheme. Numerical experiments for one-, two-, and three-dimensional cases of the fractional problem are conducted to validate the accuracy and stability of the scheme. Our approach is show-cased by solving several Gordon-type models of practical interest, including the fractional versions of sine-, sinh-, and Klein-Gordon equations, together with the numerical simulations of the collisions of the Gordon-type solitons. The simulation results can provide a deeper understanding of the complicated nonlinear behaviors of the Gordon-type solitons.
报告人简介：
郭士民，西安交通大学副教授，硕士生导师，现任西安交通大学计算数学系副系主任；2013年12月毕业于西安交通大学数学与统计学院并获博士学位，并于2011年9月至2012年9月在荷兰数学与计算机科学国家研究中心进行博士联合培养；2014年至2017年在西安交通大学能源与动力工程学院做博士后，合作导师为何雅玲院士。主要研究方向为分数阶微分方程的高精度数值算法、谱方法及计算等离子体物理学，已发表 SCI 论文27篇，其中第一作者论文24篇，单篇他引最高次数为190余次(Google学术)，另有2篇论文入选“ESI高被引论文”。攻读博士学位期间曾获2013年度教育部“博士研究生国家奖学金”，2011年度教育部“博士研究生学术新人奖”；博士学位论文入选“2016年陕西省优秀博士学位论文”；完成的“等离子体物理中非线性发展方程的数值方法研究”荣获2019年获陕西省高等学校科学技术奖一等奖 (第二完成人)。
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