讲座主题：A New Multi-Domain Spectral Method for Korteweg-de Vries Equation on The Whole Line

专家姓名：王天军

工作单位：河南科技大学

讲座时间：2023年11月7日 16:00-17:00

讲座地点：数学学院大会议室

主办单位：烟台大学数学与信息科学学院

内容摘要：

In this talk, some composite generalized Laguerre-Legendre quasi-orthogonal approximation results on the whole line are established. A novel multi-domain composite generalized Laguerre-Legendre spectral scheme is provided for the Korteweg-de Vries equation on the whole line. The scheme features mobile common boundaries of the adjacent subdomains, which better fits the soliton wave governed by the Korteweg-de Vries equation. Convergence of the proposed scheme is proved. Numerical results show the efficiency of the scheme and coincide well with theoretical analysis. Also, we apply the composite generalized Laguerre-Legendre spectral method to a nonlinear Fokker-Planck equation whose solutions may decay slowly as |x| → ∞. The problem is a coupling of hyperbolic and parabolic equations with the nonlinear term W²(v, t) and the quasilinear term W(v, t)∂xW(v, t).  In this case, our proposed method continues to work well, but the Fourier spectral method suffers.

主讲人介绍：

王天军，河南科技大学数学与统计学院教授，博士生导师，计算数学学科带头人; 河南省教育厅学术技术带头人; 长期从事偏微分方程数值方法谱方法研究工作，在《Math. Comp.)、《Adv. Comp. Math.》、《J. Sci. Comput.)、《Appl. Numer Math.》以及《Comm. Comp. Phys.》等国际著名学术期刊上发表论文四十多篇。博士论文《无界区域和外部问题的区域分解谱方法及其应用》获2009年全国百篇优秀博士论文提名论文；博士论文获上海市优秀博士论文奖。获2010年河南省第10届自然科学优秀学术论文二等奖。先后主持国家自然科学基金面上项目2项。