Log orthogonal functions in semi-infinite intervals: approximation results and applications

主讲人：陈升 北京师范大学副教授

时间：2023年3月15日16：00

地点：三号楼301

举办单位：数理学院

主讲人介绍：陈升博士，副教授。于2017年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学位论文；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-数学研究中心。

内容介绍：We construct two new classes of log orthogonal functions in semi-infinite intervals, log orthogonal functions (LOFs-II) and generalized log orthogonal functions (GLOFs-II), by applying a suitable log mapping to Laguerre polynomials. We develop basic approximation theory for these new orthogonal functions, and show that they can provide uniformly good exponential convergence rates for problems in semi-infinite intervals with slow decay at infinity. We apply them to solve several linear and nonlinear differential equations whose solutions decay algebraically or exponentially with very slow rates, and present ample numerical results to show the effectiveness of the approximations by LOFs-II and GLOFs-II.