Accuracy Enhancement Using Spectral Postprocessing for Differential Equations and Integral Equations  

作　　者：Tao Tang Xiang Xu 

机构地区：[1]Department of Mathematics,Hong Kong Baptist University,Kowloon Tong,Hong Kong [2]School of Mathematics,Fudan University,Shanghai 200433,China.

出　　处：《Communications in Computational Physics》2009年第2期779-792,共14页计算物理通讯（英文）

基　　金：The research of the first author was supported by Hong Kong Baptist University,the Research Grants Council of Hong Kong.

摘　　要：It is demonstrated that spectral methods can be used to improve the accuracy of numerical solutions obtained by some lower order methods.More precisely,we can use spectral methods to postprocess numerical solutions of initial value differential equations.After a few number of iterations(say 3 to 4),the errors can decrease to a few orders of magnitude less.The iteration uses the Gauss-Seidel type strategy,which gives an explicit way of postprocessing.Numerical examples for ODEs,Hamiltonian system and integral equations are provided.They all indicate that the spectral processing technique can be a very useful way in improving the accuracy of the numerical solutions.In particular,for a Hamiltonian system accuracy is only one of the issues;some other conservative properties are even more important for large time simulations.The spectral postprocessing with the coarse-mesh symplectic initial guess can not only produce high accurate approximations but can also save a significant amount of computational time over the standard symplectic schemes.

关 键 词：POSTPROCESSING spectral methods rate of convergence Hamiltonian system integral equations 

分 类 号：O17[理学—数学]