报告人：王冬岭讲师

        西北大学

报告题目：Two fractional differential equations and numerical methods

报告时间：2016年12月10日15:30

报告地点：实验楼105

联系人：王焰金教授

报告摘要：

Firstly, we consider time fractional ODEs. In the recent paper [D. Wang and A. Xiao, Nonlinear Dynam., 80 (2015), pp. 287-294], we established the dissipativity and contractivity of Caputo fractional nonlinear systems. We further study the corresponding numerical properties of fractional backward differentiation formula (F-BDF). We construct the F-BDFs based on popular numerical approximations to Caputo derivative, including the Grunwald-Letnikov formula, L1 method, and show that all the above methods are dissipative and constractivity, and can preserve the polynomial decay rates as the continuous problem. Finally, some numerical examples are given to illustrate the advantages of the numerical methods, and some possible extensions are also discussed.

Secondly, We consider the space fractional nonlinear Schrodinger equations (NLS) with period boundary conditions. The Strang splitting and Fourier collocation spectral methods are developed. The advantages of this method are that we can effectively dealt with the nonlocal Laplacian and the nonlinear term separately, and is explicit and unconditionally stable in time and high accurate in space. The nonlocal fractional Laplacian becomes a fully diagonal representation as the classical Laplacian, which significant reduces the computation cost and storage in numerical simulations compared with the fractional difference schemes. The convergence in L2 is proved in the framework of Lady Windermere’s fan arguments. The second-order error bound in the time semidiscretization and some local error bounds in the space semidiscretization are derived to get the the global errors. Numerical examples are given to confirm the theoretical results and to reveal the differences between fractional NLS and classical ones.

报告人简介：

王冬岭，博士，现为西北大学数学学院和非线性科学研究中心讲师。2007年、2013年于湘潭大学分别获学士、博士学位。曾访问香港中文大学、香港浸会大学等。王冬岭博士的研究方向为分数阶微分方程数值方法和动力系统保结构算法，其研究成果发表论文十余篇，发表在JCP等杂志。

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