报告人：陈升副教授

报告题目：An efficient spectral method for singular problems and singularly perturbed problems

报告摘要：

(1) In this talk, an efficient spectral method will be proposed for solving singular problems and singularly perturbed problems. Based on the Log mapping to Laguerre, the new bases are capable of exponentially approximating one-point singular functions and some boundary layer functions. The related Log spectral methods are applied to some fundamental singular problems and singularly perturbed problems, respectively. The numerical experiments are demonstrated to verify the high-efficiency of the new method.

(2) Usual spectral methods are not effective for singularly perturbed problems and singular integral equations due to the boundary layer functions or weakly singular solutions. To overcome this difficulty, the enriched spectral-Galerkin methods (ESG) are applied to deal with a class of singularly perturbed problems and singular integral equations for which the form of leading singular solutions can be determined. In particular, for easily understanding the technique of ESG, the detail of the process are provided in solving singularly perturbed problems. Numerical examples verify the efficiency and accuracy of the enriched spectral Galerkin methods

报告时间：2022年6月18日10:00-13:00

报告形式：腾讯会议；会议号：809-655-954

报告人简介：陈升，2017年博士毕业于厦门大学计算数学专业，主要从事谱方法及其对奇性问题应用的研究，其博士论文获福建省优秀博士论文；2017年毕业后入职江苏师范大学。2018年获国家创新博士后创新计划资助加入北京计算科学研究中心开展博士后工作；2021年8月入职北京师范大学自然科学高等研究院。