一、题目：

Global sixth-order quasi-compact difference methods without derivatives of source term

二、主讲人：

孙海卫

三、摘要：

Sixth-order compact difference schemes have been widely investigated in the literature. Nevertheless, those methods are all constructed based on knowing the exact values of the derivatives of the source term. Therefore, this drawback mostly prevents their actual applications as the analytic form of the source term is rarely available. In this talk, we propose global sixth-order quasi-compact difference (QCD) methods, without having to know the derivatives of the source term, for solving several PDEs. Our strategy is to discretize the equation by the fourth-order compact scheme at the improper interior grid points that adjoin the boundary, while the sixth-order scheme, where it is compact only for the unknowns, is exploited to the proper interior grid points that are not adjoining the boundary. Theoretically, we rigorously prove that the proposed method can achieve the global sixth-order accuracy for the Poisson equations and the modified Helmholtz equations. Since there are no derivatives of the source term involved in the proposed scheme, our global sixth-order quasi-compact difference method can be developed to solve the time-dependent problems using a time advancing scheme. Numerical experiments are carried out to demonstrate the convergence order and the efficiency of the proposed methods.

四、主讲人简介：

孙海卫，澳门大学数学系教授、博士生导师，1996年毕业于香港中文大学数学系获得博士学位。主要研究领域包括数值线性代数、偏微分方程数值解和计算金融学等。在SISC，SINUM，SIMAX，JCP等计算数学杂志发表超过100篇高水平研究论文，担任国际学术期刊IJCM编委，于2018年获得澳门特区政府颁发的自然科学二等奖，共主持澳门科技发展基金6项。

五、邀请人：

曾凡海 数学学院教授

六、时间：

12月6日（周二）19:00-22:00

七、地点：

腾讯会议

八、联系人：

曾凡海，联系方式：fanhai_zeng@sdu.edu.cn

九、主办：

山东大学数学学院