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学术报告-汪志波

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2020-12-07 09:56:00

学术报告


题      目: A fast linearized finite difference method for the nonlinear multi-term time-fractional wave equation


报  告  人:汪志波   副教授  (邀请人:黎稳 )

                                   广东工业大学



时      间:2020-12-07 16:00--17:00


地      点:学院401


报告人简介:

        汪志波,博士,副教授,硕士生导师,广东省“珠江人才计划”引进高层次人才,SCI期刊《Mathematical Problems in Engineering》编委,广东省青年科学家协会理事,广东省计算数学会理事。主要从事偏微分方程数值解法等方面的研究。2016年1月以“青年百人A类”人才计划加入广东工业大学,主持国家自然科学基金2项、广东省自然科学基金2项等8项科研项目,以第一或通讯作者发表28篇SCI论文,其中ESI高被引论文2篇,H指数11,i10指数13。

摘      要:

       In this paper, we study a fast and linearized finite difference method to solve the nonlinear time-fractional wave equation with multi fractional orders. We first propose a discretization to the multi-term Caputo derivative based on the recently established fast ${\cal L}2$-$1_\sigma$ formula and a weighted approach. Then we apply the discretization to construct a fully fast linearized discrete scheme for the nonlinear problem under consideration. The nonlinear term, which just fulfills the Lipschitz condition, will be evaluated on the previous time level. Therefore only linear systems are needed to be solved for obtaining numerical solutions. The proposed scheme is shown to have second-order unconditional convergence with respect to the discrete $H^1$-norm. Numerical examples are provided to justify the efficiency.