Time-space spectral method for the parabolic equation and its application in an inverse problem


主講人:馬和平  上海大學教授 博士生導師




主講人介紹:馬和平教授是理學院數學系教授,博士生導師。在非線性偏微分方程譜方法穩定性理論; N-S 方程譜和有限元混合方法的 BB 條件;  Legnedre-Chebyshev 偶合譜方法; Petrov-Galerkin 譜方法等方面做出了突出的研究工作。其研究成果得到美國 NOVA  科學出版社主編 F. Columbus 教授、美國 UCLA 的 E. Tadmor 教授、美國 Brown 大學 D.Gottlieb  教授等國際著名專家的高度評價。

內容介紹:Time-space spectral methods based on the Legendre-tau and Chebyshev collocation  approximation are introduced for solving the parabolic equation and some other  evolutionary equations. The methods adopt the advantages of both good stability  of the Legendre method and easy implementation of the Chebyshev method.  Numerical analysis and error estimates are discussed. The method is then applied  to the parabolic inverse problem with a control parameter. Numerical examples  are given to show the efficiency of the methods.