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：99精品视频在线观看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。
