The Lanczos-Chebyshev Pseudospectral Method for Solution of Differential Equations

作     者：Peter Y. P. Chen Peter Y. P. Chen

作者机构：School of Mechanical and Manufacturing Engineering University of New South Wales Sydney Australia 

出 版 物：《Applied Mathematics》 (应用数学（英文）)

年 卷 期：2016年第7卷第9期

页      面：927-938页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Solution of Differential Equations Chebyshev Economized Power Series Collocation Point Selection Lanczos-Chebyshev Pseudospectral Method 

摘      要：In this paper, we propose to replace the Chebyshev series used in pseudospectral methods with the equivalent Chebyshev economized power series that can be evaluated more rapidly. We keep the rest of the implementation the same as the spectral method so that there is no new mathematical principle involved. We show by numerical examples that the new approach works well and there is indeed no significant loss of solution accuracy. The advantages of using power series also include simplicity in its formulation and implementation such that it could be used for complex systems. We investigate the important issue of collocation point selection. Our numerical results indicate that there is a clear accuracy advantage of using collocation points corresponding to roots of the Chebyshev polynomial.