講座主題：A New Multi-Domain Spectral Method for Korteweg-de Vries Equation on The Whole Line
專家姓名：王天軍
工作單位：河南科技大學
講座時間：2023年11月7日 16:00-17:00
講座地點：數學學院大會議室
主辦單位：煙臺大學數學與信息科學學院
內容摘要：
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.
主講人介紹：
王天軍，河南科技大學數學與統計學院教授，博士生導師，計算數學學科帶頭人; 河南省教育廳學術技術帶頭人; 長期從事偏微分方程數值方法譜方法研究工作，在《Math. Comp.)、《Adv. Comp. Math.》、《J. Sci. Comput.)、《Appl. Numer Math.》以及《Comm. Comp. Phys.》等國際著名學術期刊上發表論文四十多篇。博士論文《無界區域和外部問題的區域分解譜方法及其應用》獲2009年全國百篇優秀博士論文提名論文；博士論文獲上海市優秀博士論文獎。獲2010年河南省第10屆自然科學優秀學術論文二等獎。先后主持國家自然科學基金面上項目2項。
