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


主讲人:马和平  上海大学教授 博士生导师




主讲人介绍:马和平教授是理学院数学系教授,博士生导师。在非线性偏微分方程谱方法稳定性理论; N-S 方程谱和有限元混合方法的 BB 条件;  Legnedre-Chebyshev 偶合谱方法; Petrov-Galerkin 谱方法等方面做出了突出的研究工作。其研究成果得到美国 NOVA  科学出版社主编 F. Columbus 教授、美国 UCLA 的 E. Tadmor 教授、美国 Brown 大学 D.Gottlieb  教授等国际著名专家的高度评价。

内容介绍: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.