Speaker: Dr. Sheng Chen (陈升博士)

Time: 13:00-14:00, 25 March 2021 (Thursday) (Beijing time)

Venue: B414, Lijiao Building

Abstract

We present a new class of orthogonal functions, log orthogonal functions (LOFs), which are constructed by applying a log mapping to the Laguerre functions. We develop basic approximation theory for these new orthogonal functions and compare the new basis with the classical orthogonal polynomials. The error analysis and numerical results show that the method based on the new orthogonal functions is particularly suitable for functions which have weak singularities at one endpoint, and can lead to exponential convergent rates, as opposed to low algebraic rates if usual orthogonal polynomials are used. Further, we apply them to several typical fractional differential equations whose solutions exhibit weak singularities. Numerical experiments fully support the theoretical results and show the efficiency of the proposed spectral Galerkin method.

About Dr. Chen

陈升博士师从沈捷教授，研究方向为偏微分方程数值解法，主要研究谱方法。2017年于厦门大学获得博士学位，2018年获国家创新博士后计划支持加入北京计算科学研究中心开展为期两年的博士后工作，合作导师是张智民教授。现任职江苏师范大学。主要科研获奖有：福建省第十三届自然科学优秀学术论文一等奖、福建省优秀博士学位论文、江苏省工业与应用数学学会优秀论文奖与2018年国家博士后创新人才。目前主持国家自然科学基金与江苏省自然科学基金各一项，同时完成两项博士后基金的结题工作。主要研究成果在Math. Comp.,SIAM J.Sci.Comp., Journal of Scientific Computing 等期刊上发表。