The Global Behavior of Finite Difference-Spatial Spectral Collocation Methods for a Partial Integro-differential Equation with a Weakly Singular Kernel  

作　　者：Jie Tang Da Xu 

机构地区：[1]College of Mathematics and Computer Science,Hunan Normal University,Changsha 410081,Hunan,P.R.China [2]College of Science,Hunan University of Technology,Zhuzhou 412008,Hunan,P.R.China

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2013年第3期556-570,共15页高等学校计算数学学报（英文版）

基　　金：The first author was supported in part by Scientific Research Fund of Hunan Provincial Education Department of China(10C0654);the NSF of China(10971059,11101136);the NSF of Hunan Province,China(10JJ6003);the Grant of Science and Technology Commission of Hunan Province,China(2012FJ4116);the NSF of Hunan University of Technology(2011HZX17);The second author was supported in part by NSF of China(10271046,10971062).

摘　　要：The z-transform is introduced to analyze a full discretization method fora partial integro-differential equation (PIDE) with a weakly singular kernel. In thismethod, spectral collocation is used for the spatial discretization, and, for the time stepping, the finite difference method combined with the convolution quadrature rule isconsidered. The global stability and convergence properties of complete discretizationare derived and numerical experiments are reported.

关 键 词：Partial integro-differential equation weakly singular kernel spectral collocation methods Z-TRANSFORM convolution quadrature 

分 类 号：O17[理学—数学]